- (a) Prove that
$$2 \cot 2 x + \tan x \equiv \cot x \quad x \neq \frac { n \pi } { 2 } , n \in \mathbb { Z }$$
(b) Hence, or otherwise, solve, for \(- \pi \leqslant x < \pi\),
$$6 \cot 2 x + 3 \tan x = \operatorname { cosec } ^ { 2 } x - 2$$
Give your answers to 3 decimal places.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
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