(a)[6]
Write $4\cos\theta\sin(\theta + 30^\circ)$ in the form $R\cos(2\theta - \alpha) + k$, where $R > 0$, $0^\circ < \alpha < 90^\circ$ and $k$ is a constant.
(b)[5]
Hence solve the equation $12\cos 2\phi\sin(2\phi + 30^\circ) = 5$ for $0^\circ < \phi < 90^\circ$.