I've got a random number generator that yields values between 0 and 1, and I'd like to use it to select a random point on the surface of a sphere where all points on the sphere are equally likely.
Selecting the longitude is easy as all lines of longitude are of equal length. x × 360°.
Latitude, on the other hand, requires that 0° (the equator) is twice as likely to be selected than 60°. 90° would have an almost zero chance of being selected.