Well the camera stores the transformations in a 4x4 matrix as usual, with the vec3 in the first, second, and third columns being the X, Y, and Z rotations respectively. The vec3 in the fourth column is the translation. You could probably get the angle from those....somehow.

A visual example:

However, you shouldn't be doing transformations cumulatively. You should be rebuilding the matrix from identity every frame, requiring you to store your own rotations and translations. This is to avoid accumulating rounding errors.