(a)[3]
Write $\sqrt{7}\sin x + 2\cos x$ as $R\sin(x + \alpha)$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$. Give the exact value of $R$ and state $\alpha$ correct to $2$ decimal places.
(b)[5]
Hence solve for $0^\circ < \theta < 180^\circ$ the equation $\sqrt{7}\sin 2\theta + 2\cos 2\theta = 1$.