(a)(i) Show that \(\dfrac{\operatorname{cosec}\theta-\operatorname{cot}\theta}{\sin\theta}=\dfrac{1}{1+\cos\theta}\).

(a)(ii) Hence solve \(\dfrac{\operatorname{cosec}\theta-\operatorname{cot}\theta}{\sin\theta}=\dfrac52\) for \(180^\circ\lt \theta\lt 360^\circ\).

(b) Solve \(\tan(3\phi-4)=-\dfrac12\) for \(0\lt \phi\lt \frac{\pi}{2}\) radians.