What a nice cosines sum!

Geometry Level 3

If \[\large{\displaystyle \cos^2(1˚)+\cos^2(2˚)+\cos^2(3˚)+\dots+\cos^2(90˚)=\frac{a}{b}},\] where \(a\) and \(b\) are positive co-prime integers, find \(a+b\).

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