Summation + Trigonometry

Geometry Level 3

n=118cos2(5n)\large\sum _{n=1}^{18} \cos ^{ 2 }(5n^{\circ})

Find the value of the summation above.

If the answer is of the form ab\frac{a}{b}, where aa and bb are positive coprime integers, find a+ba+b.

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