Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 15E / f / Solution

The product of reflections in two lines meeting at angle $\theta$ is a rotation through $2\theta$. Here $Q=-R_{|\Omega ⟩}{R}_g$ rotates toward the good axis by $2\theta$. Since $|\Omega ⟩$ initially makes angle $\theta$ with the bad axis,A single use replaces the angle $\theta$ by $3\theta$.