I don't have a script to put down as I'm looking for a straight-forward answer/explanation. I do not need for you to give me a script, more so point me in the right direction.
you can find the CFrame of the Camera simply by doing
workspace.CurrentCamera.CFrame
From this point on you can do a lot of things, like get the LookVector of the camera, or if like in the question, you want the rotation of it, you can use toAxisAngle
local CameraRotation = workspace.CurrentCamera.CFrame:toAxisAngle()
EDIT: Although obvious to some, it should be noted that this script will only work from the Client.