6.
$$f ( \theta ) = 4 \cos ^ { 2 } \theta - 3 \sin ^ { 2 } \theta$$
- Show that \(f ( \theta ) = \frac { 1 } { 2 } + \frac { 7 } { 2 } \cos 2 \theta\).
- Hence, using calculus, find the exact value of \(\int _ { 0 } ^ { \frac { \pi } { 2 } } \theta \mathrm { f } ( \theta ) \mathrm { d } \theta\).