Show that the equation
$$2 \cot ^ { 2 } x + 5 \operatorname { cosec } x = 10$$
can be written in the form \(2 \operatorname { cosec } ^ { 2 } x + 5 \operatorname { cosec } x - 12 = 0\).
Hence show that \(\sin x = - \frac { 1 } { 4 }\) or \(\sin x = \frac { 2 } { 3 }\).
Hence, or otherwise, solve the equation
$$2 \cot ^ { 2 } ( \theta - 0.1 ) + 5 \operatorname { cosec } ( \theta - 0.1 ) = 10$$
giving all values of \(\theta\) in radians to two decimal places in the interval \(- \pi < \theta < \pi\).
(3 marks)