This question is very elementary when compared to the level of problems asked on this site. However, I am preparing for the Joint Entrance Examination in India and I needed some help in finding an approach and I would like to solicit the answer as well.
The value of $$\sum_{k=1}^{13} \frac{1}{\sin\left(\frac{\pi}{4}+\frac{(k-1)\pi}{6}\right) \sin\left(\frac{\pi}{4}+\frac{k\pi}{6}\right)}=?$$
Also, I would greatly appreciate it if your answer includes mathematics used in junior high.