Summation!

Geometry Level 5

\[\large \sum_{m=1}^{6}\csc\left(\omega+\frac{(m-1)\pi}{4}\right)\csc\left(\omega+\frac{m\pi}{4}\right)=4\sqrt{2}\] For \(0<\omega<\frac{\pi}{3}\) , find \[\sum_{r=1}^{7}\tan^{2}(\frac{3r\omega}{4})\]

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