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JEE Advanced 2016 Paper 2 Mathematics Question 39

The value \(\displaystyle\sum_{k=1}^{13}\frac{1}{\text{sin}{\left(\frac{\pi}{4} + \frac{(k-1)\pi}{6}\right)}\text{sin}{\left(\frac{\pi}{4} + \frac{k\pi}{6}\right)}}\) is equal to

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