$\frac{1}{7\operatorname{cosec}^{2}(7\theta)}{\sum_{k=0}^{6} \operatorname{cosec}^{2}(\theta+\frac{k\pi}{7})}$

Question

Here, $\theta = \frac{\pi}{8}$. This question is from a book recommended for preparing for the JEE Advance exam. I tried converting the series like, $$\frac{1}{\sin^{2}(\theta+\frac{k\pi}{7})}=\frac{2}{1-\cos(2\theta+\frac{2k\pi}{7})}$$ But this didn't lead to anything. Then I also tried taking the $k=0$ term out and pair up first and last terms which still didn't lead to anything. This looks like a very interesting problem and help would be highly appreciated.