8 (i) By first expanding $\sin ( 2 \theta + \theta )$, show that

$$\sin 3 \theta = 3 \sin \theta - 4 \sin ^ { 3 } \theta$$

(ii) Show that, after making the substitution $x = \frac { 2 \sin \theta } { \sqrt { 3 } }$, the equation $x ^ { 3 } - x + \frac { 1 } { 6 } \sqrt { } 3 = 0$ can be written in the form $\sin 3 \theta = \frac { 3 } { 4 }$.\\
(iii) Hence solve the equation

$$x ^ { 3 } - x + \frac { 1 } { 6 } \sqrt { } 3 = 0$$

giving your answers correct to 3 significant figures.

\hfill \mbox{\textit{CAIE P3 2014 Q8}}