Applying every concept we know

Geometry Level 5

\[\displaystyle\sum_{k=1}^{49} \cot^{2} \left( \dfrac{(2k+1)\pi}{100}\right)\]

If the summation above can be expressed as \(\left( a-\csc^{2} \left( \dfrac{\pi}{b}\right)\right)\) for positive integers \(a,b\), find \(a+b\).

Inspiration.
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