I have a rotation as a right-handed coordinate system and a right-handed rotation through an angle $\gamma$ around $z$-axis, an angle $\beta$ around $y$-axis and an angle $\alpha$ around $x$-axis. I am wondering if this rotation can be rewritten as a rotation with angles $\theta_1$ in $yz$-axis (around $x$-axis) and $\theta_2$ in $xy$-plane (around z-axis)?
It seems yes, as I checked by several example. f it is true then, how I can prove it?
To prove you can use the linear transformations, basically write the rotation matrices for any angle then it will be easy to show the equality. For more general proof you can simply analyse the linear dependence relation for your rotation matrices.