For some of you this could be a really easy question, but I didn’t find a solution or was too dumb to understand some of the math papers.

I am currently working in Python but that shouldn’t matter.
What I want is to get the rotation angle of the unit vector representing the rotation, over a specific axis.

Example:

I have the Vector (1.0, 0, 0) and I know this represents the rotation over Y-axis.
Or the Vector (0, 0, -1) which is the representation for a rotation over Z-axis.

How do I get the angles represented by these vectors?