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Geometry Level 5

T(r,θ)=sin(rθ)k=0r1sin(θ+kπr) \large T(r,\theta)= \frac{\sin(r \theta)}{ \displaystyle \prod_{k=0}^{r-1} \sin \left (\theta +\frac{k\pi }{r} \right )}

Let S(n,θ)=r=1nT(r,θ) \displaystyle S(n,\theta)=\sum_{r=1}^{n}T(r,\theta) . Find the value of S(6,1)+T(7,2) S(6,1) + T(7,2) .

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