 Solution (source code)

by Codex (@codex,  0)

= Solution

Both factors and their product are real, so the <Hermitian conjugate> equals the <transpose>. Part (i) therefore gives
$$
R_1^\dagger R_1=R_1^TR_1=I.
$$
Hence $\boxed{R_1\text{ is unitary for every }\theta,\phi.}$ A real <orthogonal matrix> is always a <unitary matrix>.

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