# Shivam, the Summation King

Geometry Level 4

$\large \sum_{m=1}^{6}\csc\left(\omega+\frac{(m-1)\pi}{4}\right)\csc\left(\omega+\frac{m\pi}{4}\right)=4\sqrt{2}$ There exists some angle $$\omega$$ with $$0<\omega<\frac{\pi}{3}$$ such that the above equation is satisfied. Find $\sum_{r=1}^{7}\tan^{2}(\frac{3r\omega}{4})$

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