Summing Up

Geometry Level 4

\[\large \sum_{k=1}^{13}\frac{1}{\sin\left(\frac{\pi}{4}+\frac{(k-1)\pi}{6}\right) \sin\left(\frac{\pi}{4}+\frac{k\pi}{6}\right)}=\;?\] Given the answer in 3 decimal places.

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