Evaluate: $\sum _{r=1}^{13}\frac{1}{\sin \left[\frac{\pi }{4}+(r-1)\frac{\pi }{6}\right]\sin \left[\frac{\pi }{4}+\frac{r\pi }{6}\right]}$

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Evaluate: \(\sum _{r=1}^{13}\frac{1}{\sin \left[\frac{\pi }{4}+(r-1)\frac{\pi }{6}\right]\sin \left[\frac{\pi }{4}+\frac…