- (i) Use an appropriate double angle formula to show that
$$\operatorname { cosec } 2 x = \lambda \operatorname { cosec } x \sec x$$
and state the value of the constant \(\lambda\).
(ii) Solve, for \(0 \leqslant \theta < 2 \pi\), the equation
$$3 \sec ^ { 2 } \theta + 3 \sec \theta = 2 \tan ^ { 2 } \theta$$
You must show all your working. Give your answers in terms of \(\pi\).