8 The first term of a progression is \(\sin ^ { 2 } \theta\), where \(0 < \theta < \frac { 1 } { 2 } \pi\). The second term of the progression is \(\sin ^ { 2 } \theta \cos ^ { 2 } \theta\).
- Given that the progression is geometric, find the sum to infinity.
It is now given instead that the progression is arithmetic. - Find the common difference of the progression in terms of \(\sin \theta\).
- Find the sum of the first 16 terms when \(\theta = \frac { 1 } { 3 } \pi\).