The angular distortion is straightforward. It's simple mathematics to calculate the angle of a photon's path to the direction of the moving observer's frame of reference at any given velocity. This is what constitutes relativistic aberration.
The colour shift is simple if one is dealing with pure longitutional or pure transverse motion. A combination of the two in a flyby scenario however requires careful thought.
It's analogous to knowing the answer is grey but what shade of grey.
Regards
Steven