9. (a) Express \(2 \sin \theta - 4 \cos \theta\) in the form \(R \sin ( \theta - \alpha )\), where \(R\) and \(\alpha\) are constants, \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\) Give the value of \(\alpha\) to 3 decimal places. $$H ( \theta ) = 4 + 5 ( 2 \sin 3 \theta - 4 \cos 3 \theta ) ^ { 2 }$$ Find
(b) (i) the maximum value of \(\mathrm { H } ( \theta )\),
(ii) the smallest value of \(\theta\), for \(0 \leqslant \theta < \pi\), at which this maximum value occurs. Find
(c) (i) the minimum value of \(\mathrm { H } ( \theta )\),
(ii) the largest value of \(\theta\), for \(0 \leqslant \theta < \pi\), at which this minimum value occurs.