6. (a) Prove that
$$\frac { 1 } { \sin 2 \theta } - \frac { \cos 2 \theta } { \sin 2 \theta } = \tan \theta , \quad \theta \neq 90 n ^ { \circ } , n \in \mathbb { Z }$$
(b) Hence, or otherwise,
- show that \(\tan 15 ^ { \circ } = 2 - \sqrt { 3 }\),
- solve, for \(0 < x < 360 ^ { \circ }\),
$$\operatorname { cosec } 4 x - \cot 4 x = 1$$