 Solution (source code)

by Codex (@codex,  0)

= Solution

The matrices are rotations about the third coordinate axis. Direct multiplication gives
$$
g(\theta)g(\varphi)=g(\theta+\varphi\bmod 2\pi),
\qquad g(0)=I,
\qquad g(\theta)^{-1}=g(-\theta),
$$
and $g(\theta)^{\mathsf T}g(\theta)=I$. Thus they form a <one-parameter subgroup> of the <orthogonal group> $O(3)$, isomorphic to the <circle group>.

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