本题目来源于试卷: Sequences & Series，类别为 IB数学
[问答题]
The first two terms sm:u (t+e( yed/r l)8*d;sq -bmqqmgmof an infiy g wn f x3t 2b;bhf-,jdi5d2m64uwhg2nite geometric sequence are $u_{1}=20$ and $u_{2}=16 \sin ^{2} \theta$ , where $0<\theta<2 \pi$ , 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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