(a)(i) Show that

\(\frac{1}{\operatorname{sec}\theta-1}-\frac{1}{\operatorname{sec}\theta+1}=2\operatorname{cot}^2\theta.\)

(a)(ii) Hence solve

\(\frac{1}{\sec2x-1}-\frac{1}{\sec2x+1}=6\)

for \(-90^\circ\lt x\lt90^\circ\).

(b) Solve

\(\operatorname{cosec}\left(y+\frac{\pi}{3}\right)=2\)

for \(0\leq y\leq2\pi\) radians, giving your answers in terms of \(\pi\).