本题目来源于试卷: Trigonometric Functions，类别为 IB数学
[问答题]
The first two terms of an infinite geometricuqe2 j 2meuv/h +//oe53k x 0 ,woa8hwopg;uezh ,tp9 fpbf xku(nrf(cv.;*3z sequence are $ u_{1}=20$ and $u_{2}=16 \sin ^{2} \theta$, where $0 \lt \theta \lt 2 \pi$ , and $\theta \neq \pi$ .
1. 1. Find an expression for r in terms of $\theta$ .
2. Find the possible values of r .
2. Show that the sum of the infinite sequence is $\frac{100}{3+2 \cos 2 \theta}$
3. Find the values of $\theta$ which give the greatest value of the sum.
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