6 Let \(I = \int _ { 0 } ^ { 3 } \frac { 27 } { \left( 9 + x ^ { 2 } \right) ^ { 2 } } \mathrm {~d} x\).
- Using the substitution \(x = 3 \tan \theta\), show that \(I = \int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \cos ^ { 2 } \theta \mathrm {~d} \theta\).
- Hence find the exact value of \(I\).