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

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

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