I made this thread earlier but unfortunately let it sit too long without checking. Thank you to the anon who was trying to work with me. I have since made a better representation of the information I am providing. But anyways...

This webm is a visualization of what I currently have set up in Unity:

The red pyramid and torus represent the player character and it's rotation around a centerpoint. The player is facing the direction of it's rotation around said centerpoint.
The green camera, green torus, and yellow torus represent the camera's current rotation that I was able to achieve in relation to both the player and the centerpoint.
The cyan camera, cyan torus, and yellow torus represent my desired rotation for the camera in relation to both the player and the centerpoint.

My question is, mathematically, how do I go about getting the green camera's rotation around the centerpoint to match the cyan camera's rotation around the centerpoint? Any resources that I can be pointed towards would be much appreciated.