(i) Show that

\(\frac{\operatorname{cosec}\theta}{\operatorname{cot}\theta+\tan\theta}=\cos\theta.\)

It is given that

\(\int_0^a \frac{\operatorname{cosec}2\theta}{\cot2\theta+\tan2\theta}\,d\theta=\frac{\sqrt3}{4}, \qquad 0\lt a\lt \frac{\pi}{4}.\)

(ii) Using your answer to part (i), find \(a\) in terms of \(\pi\).