Using Levi-civita symbol to determine axis and angle of rotation matrix

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One of the questions on the course involves finding the angle and axis of this rotation matrix;

$$R = \gamma\ \begin{pmatrix} 0 & -2 & 1\\ 2 & 0 & 0\\ -1 & 0 & 0 \end{pmatrix}$$

My lecturer solves this in an example that reads;

$$ \omega_i = -\frac{1}{2} \epsilon_{ijk}R_{jk} $$

$$ \omega_i = (R_{23},R_{31},R_{12})_i = \omega n_i $$

Therefore the angle is $|\underline{\omega}| = \sqrt{5} \gamma$ and axis is $ \underline{n} = \frac{1}{\sqrt{5}}(0,1,2)$

Two questions;

  1. What is $\omega$?
  2. Is this method limited to this case or can it be applied generally?