8. (i) Solve, for $- 180 ^ { \circ } \leqslant x < 180 ^ { \circ }$,

$$\tan \left( x - 40 ^ { \circ } \right) = 1.5$$

giving your answers to 1 decimal place.\\
(ii) (a) Show that the equation

$$\sin \theta \tan \theta = 3 \cos \theta + 2$$

can be written in the form

$$4 \cos ^ { 2 } \theta + 2 \cos \theta - 1 = 0$$

(b) Hence solve, for $0 \leqslant \theta < 360 ^ { \circ }$,

$$\sin \theta \tan \theta = 3 \cos \theta + 2$$

showing each stage of your working.\\

\hfill \mbox{\textit{Edexcel C2 2013 Q8 [11]}}