(a(i))[3]
In the geometric case, the sum to infinity is $\frac{1}{\cos \theta}$. Show that the second term is $\cos \theta \sin^2 \theta$.
(a(ii))[2]
Find the sum of the first 12 terms when $\theta = \tfrac{1}{3}\pi$, and round your answer to 4 significant figures.
(b)[4]
In the arithmetic case, the first two terms are still $\cos \theta$ and $\cos \theta \sin^2 \theta$ respectively. Find the 85th term when $\theta = \tfrac{1}{3}\pi$.