Summation + Trigonometry

Geometry Level 3

\[\large\sum _{n=1}^{18} \cos ^{ 2 }(5n^{\circ})\]

Find the value of the summation above.

If the answer is of the form \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, find \(a+b\).

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