4 It is given that \(2 \operatorname { cosec } ^ { 2 } x = 5 - 5 \cot x\).
- Show that the equation \(2 \operatorname { cosec } ^ { 2 } x = 5 - 5 \cot x\) can be written in the form
$$2 \cot ^ { 2 } x + 5 \cot x - 3 = 0$$
- Hence show that \(\tan x = 2\) or \(\tan x = - \frac { 1 } { 3 }\).
- Hence, or otherwise, solve the equation \(2 \operatorname { cosec } ^ { 2 } x = 5 - 5 \cot x\), giving all values of \(x\) in radians to one decimal place in the interval \(- \pi < x \leqslant \pi\).