Rotation equation

I am trying to solve the rotation matrix equation. The problem is that I rotate a input point a (X,Y,X) to get output point b (X’,Y’,Z’) by rotating X Axis (theta), Y-Axis (alpha) and Z-axis omega.

I got the 3 linear equations of 3 sine and cos angles and along with XYZ, X’Y’Z’ values.

How do I solve the matrix equation to get
theta, alpha and omega. Is there any straight forward equation.

have a look to see if this is of any help…