(a)(i) Show that

\(\frac{1}{(1+\operatorname{cosec}\theta)(\sin\theta-\sin^2\theta)} =\operatorname{sec}^2\theta.\)

(a)(ii) Hence solve

\((1+\operatorname{cosec}\theta)(\sin\theta-\sin^2\theta)=\frac34\)

for \(-180^\circ\leq\theta\leq180^\circ\).

(b) Solve

\(\sin\left(3\phi+\frac{2\pi}{3}\right)=\cos\left(3\phi+\frac{2\pi}{3}\right)\)

for \(0\leq\phi\leq\dfrac{2\pi}{3}\) radians, giving your answers in terms of \(\pi\).