(i)[2]
Show that $\sin 2x \cot x \equiv 2\cos^2 x$.
(ii(a))[4]
Using the identity in part (i), find the least possible value of $3\sin 2x \cot x + 5\cos 2x + 8$ as $x$ varies.
(ii(b))[5]
Using the identity in part (i), find the exact value of $\int_{\frac{1}{8}\pi}^{\frac{1}{6}\pi} \cosec 4x \, \tan 2x \, dx$.