The initial term of the progression is $\sin^2 \theta$, with $0 < \theta < \tfrac{1}{2}\pi$. Its second term is $\sin^2 \theta \cos^2 \theta$.
(a)[3]
Since the progression is geometric, determine the sum to infinity.
(b(i))[3]
The progression is now stated to be arithmetic instead. Determine the common difference in terms of $\sin \theta$.
(b(ii))[3]
Determine the sum of the first 16 terms when $\theta = \tfrac{1}{3}\pi$.
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