(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 smallest 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 the working needed and giving the answers correct to 2 decimal places.