In general, how an element $g \in SO(3)$ is characterized?
I know that we are talking about $3D$ rotation matrices, hence I guess that $g=\textbf{R}_g \in \mathbb{R}^{3 \times 3}$.
But explicitly, is $g \in SO(3)$ generally parametrized by three angles $\alpha,\beta, \gamma$?
Then, how should we express a transformation of this kind?