(a) Solve \(2\operatorname{cot}(z+35^\circ)=5\) for \(0^\circ\leq z\leq360^\circ\).

(b) (i) Show that \(\dfrac{\operatorname{sec}\theta}{\operatorname{cot}\theta+\tan\theta}=\sin\theta\).

(ii) Hence solve \(\dfrac{\operatorname{sec}3\theta}{\operatorname{cot}3\theta+\tan3\theta}=-\dfrac{\sqrt3}{2}\) for \(-\dfrac{\pi}{2}\leq\theta\leq\dfrac{\pi}{2}\), giving your answers in terms of \(\pi\).