(a)[4]
Express $5\sin\left(x + \tfrac{\pi}{6}\right) - 4\cos x$ as $R\sin(x - \alpha)$, where $R > 0$ and $0 < \alpha < \tfrac{\pi}{2}$. State the exact value of $R$ and give $\alpha$ correct to 3 decimal places.
(b)[4]
Hence solve the equation $5\sin\left(2\theta + \frac{\pi}{6}\right) - 4\cos 2\theta = \sqrt{7}$ for $0 \leq \theta \leq \pi$, and state both answers correct to 2 decimal places.