(a)[6]
Write $4 \cos \theta \sin(\theta + 30^\circ)$ as $R \cos(2\theta - \alpha) + k$, with $R > 0$, $0^\circ < \alpha < 90^\circ$ and $k$ constant.
(b)[5]
Hence determine the solutions of $12 \cos 2\phi \sin (2\phi + 30^\circ) = 5$ for $0^\circ < \phi < 90^\circ$.