(i)[3]
Rewrite $9\sin\theta - 12\cos\theta$ as $R\sin(\theta - \alpha)$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$. State the value of $\alpha$ correct to $2$ decimal places.
(ii)[4]
Hence solve the equation $9\sin\theta - 12\cos\theta = 4$ within $0^\circ \leq \theta \leq 360^\circ$.
(iii)[1]
State the greatest value of $k$ for which the equation $9\sin\theta - 12\cos\theta = k$ has solutions.