Question: Show that an arbitrary (2 times 2) matrix with real entries that is orthogonal and has unit determinant can always be parameterized as in Eq.

Show that an arbitrary $2 \times 2$ matrix with real entries that is orthogonal and has unit determinant can always be parameterized as in Eq. (6.3). Thus any $\mathrm{SO}(2)$ matrix can be interpreted as a rotation in some plane.

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