The Rotation Problem

Given the latitude and longitude of a prior planetary rotation axis (or pole), and given a set of latitude and longitude points defining a number of features on the surface of the planet, determine the latitude and longitude points describing the location of the features in the prior rotational regime.

I know.  Someone’s already solved this problem.  His name was Euler, and he did it in a more general case. So much more general, that all of the descriptions I can find of his solutions are a little opaque.