From axis and angle of rotation to rotation matrix

Question

I have the rotation axis $\mathbb{R} (1, 1, -1)$ and the angle $\pi/4$.

How do I compute the rotation matrix?

I know the inverse process in which you use $trace(M) = 1 - 2cos(\theta)$ to get the angle and $Ax = x$ to get the axis but I couldn't really apply that in an "inversed" way.

Answer 1

Look up Rodrigues' formula, which does exactly this.