(a) Solve the equation \(\sin x\cos x=\dfrac12\tan x\), for \(0^\circ\leq x\leq180^\circ\).

(b) (i) Prove the identity

\(\operatorname{sec}\theta-\frac{\sin\theta}{\operatorname{cot}\theta}\equiv\cos\theta.\)

(ii) Hence solve

\(\operatorname{sec}3\theta-\frac{\sin3\theta}{\cot3\theta}=\frac12\)

for \(-\dfrac{2\pi}{3}\leq\theta\leq\dfrac{2\pi}{3}\).