Don't note the factorisation of 34

Geometry Level 4

The sum

\[\sum_{n=0}^{18} \sin^2\left(\frac{34}{19} \cdot 2\pi n^2\right)\]

can be expressed in the form \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers. Find \(m+n\).

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