# TrigoNOPEmetry

Geometry Level 4

$\displaystyle \Omega_{n}(x) =\frac{\displaystyle \sum_{i=0}^n \cos \bigg[(2i+1)x \bigg]}{\displaystyle \sum_{i=0}^n \sin \bigg [ ({2i+1})x \bigg]}$

Consider the function above, if $$\displaystyle \Omega_{200}\left(\frac{\pi}{8}\right)$$ can be expressed in the form $$\sqrt{a+b\sqrt{c}}$$, where $$a,b,c$$ are positive integers, with $$b$$ square-free.

What is the value of $$a+b+c$$?

This is my 200-follower problem. It has been a very, very interesting journey so far. Thank you Brilliant!

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