Export and save photo coords (longtitude, latitude) from Android camera

My task is to create an app, which gives the opportunity to user to take a shot from mobile camera or pick a photo from gallery, export photo's geotag, and on the next step I would like to add a button which will convert these coords from mobiles datum (WGS84) to my country's datum which is EGSA87. I know it's hard for a newbie user but I'll try:'D

At the moment I finished the part of image capturing and image selection from the gallery.

I found some packages like exif, geolocation etc. but I need some help to apply them: P

The code is the following.

import 'dart:io';

import 'package:flutter/cupertino.dart';
import 'package:flutter/material.dart';
import 'package:tflite/tflite.dart';
import 'package:image_picker/image_picker.dart';

class Home extends StatefulWidget {
  @override
  _HomeState createState() => _HomeState();
}

class _HomeState extends State<Home> {
  bool _loading = true;
  File _image;
  List _output;
  final picker = ImagePicker();


  detectImage(File image) async {
    var output = await Tflite.runModelOnImage(
        path: image.path,
        numResults: 2,
        threshold: 0.6,
        imageMean: 127.5,
        imageStd: 127.5
    );
    setState(() {
      _output = output;
      _loading = false;
    });
  }

  @override
  void dispose() {
    // TODO: implement dispose
    super.dispose();
  }

  pickImage()async{
    var image = await picker.getImage(source: ImageSource.camera);
    if(image == null) return null;

    setState(() {
      _image = File(image.path);
    });

    detectImage(_image);
  }

  pickGalleryImage()async{
    var image = await picker.getImage(source: ImageSource.gallery);
    if(image == null) return null;

    setState(() {
      _image = File(image.path);
    });

    detectImage(_image);
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
        backgroundColor: Colors.blueAccent,
        body: Container(
            padding: EdgeInsets.symmetric(horizontal: 40),
            child: Column(crossAxisAlignment: CrossAxisAlignment.start,
              children: <Widget>[
                SizedBox(height: 40),
                Text('Coords Converter App',
                  style: TextStyle(color: Colors.white,
                      fontWeight: FontWeight.w500,
                      fontSize: 30),
                ),
                SizedBox(height: 5),
                Text('',
                  style: TextStyle(color: Colors.white,
                      fontSize: 10),
                ),
                SizedBox(height: 50),
                Center(child: _loading ?
                Container(
                  width: 350,
                  child: Column(children: <Widget>[
                    Image.asset('assets/new.png'),
                    SizedBox(height: 50),
                  ],),
                ) : Container(
                  child: Column(children: <Widget>[
                    Container(
                      height: 250,
                      child: Image.file(_image),
                    ),
                    SizedBox(height: 20),
                    _output != null
                        ? Text('${_output[0]['label']}',
                      style: TextStyle(
                          color: Colors.white,
                          fontSize: 15
                      ),
                    )
                        : Container(),
                    SizedBox(height: 10),
                  ],),
                ),
                ),
                Container(
                  width: MediaQuery.of(context).size.width,
                  child: Column(
                    children: <Widget>[
                      GestureDetector(
                        onTap: (){
                          pickImage();
                        },
                        child: Container(
                          width: MediaQuery.of(context).size.width - 250,
                          alignment: Alignment.center,
                          padding: EdgeInsets.symmetric(horizontal: 10, vertical: 18),
                          decoration: BoxDecoration(
                            color: Colors.redAccent,
                            borderRadius: BorderRadius.circular(6),
                          ),
                          child: Text(
                            'Capture a Photo',
                            style: TextStyle(color: Colors.white, fontSize: 16),
                          ),
                        ),
                      ),
                      SizedBox(height: 5),
                      GestureDetector(
                        onTap: (){
                          pickGalleryImage();
                        },
                        child: Container(
                          width: MediaQuery.of(context).size.width - 250,
                          alignment: Alignment.center,
                          padding: EdgeInsets.symmetric(horizontal: 10, vertical: 18),
                          decoration: BoxDecoration(
                            color: Colors.redAccent,
                            borderRadius: BorderRadius.circular(6),
                          ),
                          child: Text(
                            'Select a photo',
                            style: TextStyle(color: Colors.white, fontSize: 16),
                          ),
                        ),
                      ),
                    ],),
                ),
              ],
            )
        )
    );
  }
}