- (a) Show that
$$\cot x - \cot 2 x \equiv \operatorname { cosec } 2 x , \quad x \neq \frac { n \pi } { 2 } , \quad n \in \mathbb { Z }$$
(b) Hence, or otherwise, solve for \(0 \leqslant \theta \leqslant \pi\)
$$\operatorname { cosec } \left( 3 \theta + \frac { \pi } { 3 } \right) + \cot \left( 3 \theta + \frac { \pi } { 3 } \right) = \frac { 1 } { \sqrt { 3 } }$$
You must show your working.
(Solutions based entirely on graphical or numerical methods are not acceptable.)