Switching from fragment with map fragment leaves a black screen

I have added a full-screen map fragment to one of my three tabbed fragments. Everything works great apart from an issue I'm experiencing with switching between the tabs.

Each time I switch from the fragment with the map, to one of the other fragments, I get a black screen for like 0.2 seconds. It seems to be a similar issue to the problems with scrolling in an activity with a map fragment.

I've tried adding a transparent view other the top of the map as others have suggested, but it didn't help.

This is my xml:

<FrameLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context=".ParkMapFragment">

    <fragment
        android:id="@+id/fullParkMap"
        android:name="com.google.android.gms.maps.SupportMapFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent" />
</FrameLayout>

And this is my code:

public class ParkMapFragment extends Fragment {
    public ParkMapFragment() {
        // Required empty public constructor
    }

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                         Bundle savedInstanceState) {
        // Inflate the layout for this fragment
        return inflater.inflate(R.layout.fragment_map, container, false);
    }

    @Override
    public void onStart(){
        super.onStart();

        getActivity().setTitle("Map");
    }

    @Override
    public void onDestroyView() {
        super.onDestroyView();
        SupportMapFragment mapFragment = (SupportMapFragment) getFragmentManager().findFragmentById(R.id.fullParkMap);
        if (mapFragment != null) {
            getFragmentManager().beginTransaction().remove(mapFragment).commit();
        }
    }
}

Anyone have any suggestions?