If you want a proof of correctness, see Archimedes (225 BCE) https://en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

Cf. also http://extremelearning.com.au/how-to-generate-uniformly-random-points-on-n-spheres-and-n-balls/

This and a few other methods for picking points uniformly on the sphere, projected stereographically to the plane: https://observablehq.com/@jrus/stereorandom