Coordinates for coupled transition dipole moments

I am working on some calculations on coupled transition dipole moments interacting with light pulses with different polarisations.
I am currently trying to find a way of writing $theta_{beta}$ and $phi_{beta}$ as a function of $theta_{alpha}$,$phi_{alpha}$ and of the internal angles (which are fixed) $theta_{alphabeta}$,$phi_{alphabeta}$. By doing that I can integrate over $theta_{alpha}$,$phi_{alpha}$, and all the terms depending on $theta_{alphabeta}$,$phi_{alphabeta}$ will just be constant.
I have the feeling spherical harmonics and Carnot formulas might help but been stuck on this for a while and everything I have tried so far has not worked. Even converting to cartesian coordinates and then converting back to spherical has not given me anything useful to work with.

Any hint on how to tackle this will be much appreciated, thanks.