Actioncams have a fisheye. Therefore recorded videos are intentionally distorted. In this distortion, a range of view is encoded, by projecting it on a sphere and putting a camera in the middle, you get a horizontal field of view of about 175°.
Which software framework (xna, unity, ...) in the free version is best suited to create a program that offers to load a video file, projects this video file on a sphere and lets the user view it with his mouse or head tracker. How could you go about creating it in the software mentioned?