I have two sets of three non-collinear unit vectors which are the axes of rotation in the 3d cartesian system. The problem is how to calculate for the given rotations (alpha, beta, gamma) in the first set equivalent rotation angles in the second one? I suppose that we should take into account three cases of transformation for one, two and three points. I thought about quaternion equations but I'm not familiar with them and I can't assess is it a step in the right direction.

Any hints, papers or suggestions will be appreciated.