7 (i) Express $5 \sin 2 \theta + 2 \cos 2 \theta$ in the form $R \sin ( 2 \theta + \alpha )$, where $R > 0$ and $0 ^ { \circ } < \alpha < 90 ^ { \circ }$, giving the exact value of $R$ and the value of $\alpha$ correct to 2 decimal places.

Hence\\
(ii) solve the equation

$$5 \sin 2 \theta + 2 \cos 2 \theta = 4$$

giving all solutions in the interval $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$,\\
(iii) determine the least value of $\frac { 1 } { ( 10 \sin 2 \theta + 4 \cos 2 \theta ) ^ { 2 } }$ as $\theta$ varies.

\hfill \mbox{\textit{CAIE P2 2013 Q7}}