Extracting only z rotation matrix from a rotation matrix

Hello,
I have a 3X3 rotation matrix. I have small 3D model. I only need to consider z rotation for that model, I don’t need to consider xy movement or rotation. How can I extract the matrix that only consider z rotation of the model from the given rotation matrix?
Thanks every body in advance.

I remember I had this problem quite some time ago, it’s not trivial task, here is some info

http://paulbourke.net/geometry/transformationprojection/

(scroll down to Euler angles section, there is link to pdf ‘Extraction of Euler angles from rotation matrix’ there, it’s messy, but explains necessary math)