Geometry Level 4

Ωn(x)=i=0ncos[(2i+1)x]i=0nsin[(2i+1)x] \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 Ω200(π8) \displaystyle \Omega_{200}\left(\frac{\pi}{8}\right) can be expressed in the form a+bc\sqrt{a+b\sqrt{c}}, where a,b,ca,b,c are positive integers, with bb square-free.

What is the value of a+b+c 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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