(a(i))[3]
Express $4\sin \theta + 4\cos \theta$ as $R\sin(\theta + \alpha)$, with $R > 0$ and $0^\circ < \alpha < 90^\circ$.
(a(ii))[2]
Hence determine the least positive value of $\theta$ that satisfies $4\sin \theta + 4\cos \theta = 5$.
(b)[6]
Solve the equation $4 \cot 2x = 5 + \tan x$ for $0 < x < \pi$, showing all required steps and giving the answers correct to 2 decimal places.