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Let 0<θ<π2 0 <\theta < \dfrac \pi 2 0<θ<2π satisfying tanθ=32 \tan \theta = \sqrt{ \dfrac 32 } tanθ=23. Evaluate
1+2(1−cosθ)+3(1−cosθ)2+⋯ . 1 + 2(1-\cos \theta) + 3(1-\cos \theta)^2 + \cdots . 1+2(1−cosθ)+3(1−cosθ)2+⋯.
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