3 (i) Show that $12 \sin ^ { 2 } x \cos ^ { 2 } x \equiv \frac { 3 } { 2 } ( 1 - \cos 4 x )$.\\
(ii) Hence show that

$$\int _ { \frac { 1 } { 4 } \pi } ^ { \frac { 1 } { 3 } \pi } 12 \sin ^ { 2 } x \cos ^ { 2 } x d x = \frac { \pi } { 8 } + \frac { 3 \sqrt { } 3 } { 16 }$$

\hfill \mbox{\textit{CAIE P2 2013 Q3}}