Note the factorisation of 34

Geometry Level 5

The sum

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

can be expressed in the form \(-\dfrac{a\sqrt b}{c}\), where \(a,b\) and \(c\) are positive integers with \(a\) and \(c\) coprime and \(b\) squarefree. Find \(a+b+c\).

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