(a)(i) Show that \(\operatorname{sec}\theta-\dfrac{\tan\theta}{\operatorname{cosec}\theta}=\cos\theta\).

(a)(ii) Solve \(\operatorname{sec}2\theta-\dfrac{\tan2\theta}{\operatorname{cosec}2\theta}=\dfrac{\sqrt3}{2}\) for \(0^\circ\leq\theta\leq180^\circ\).

(b) Solve \(2\sin^2\left(\phi+\frac{\pi}{3}\right)=1\) for \(0\lt \phi\lt 2\pi\) radians.