8.
$$f ( \theta ) = 9 \cos ^ { 2 } \theta + \sin ^ { 2 } \theta$$
- Show that \(\mathrm { f } ( \theta ) = a + b \cos 2 \theta\), where \(a\) and \(b\) are integers which should be found.
- Using your answer to part (a) and integration by parts, find the exact value of
$$\int _ { 0 } ^ { \frac { \pi } { 2 } } \theta ^ { 2 } \mathrm { f } ( \theta ) \mathrm { d } \theta$$