Threejs compass based on camera rotation

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I wanted to make a compass like the one on Facebook: Click here for image

The FOV (the slice of pie in the middle of the compass) will rotate based on the FOV of the camera. I have the x, y, and z rotations of the camera, but I was wondering how to translate that into a 2d circle view? Also, the y-rotation of the three.js camera only goes from -PI / 2 to PI / 2

Any help is greatly appreciated :)

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