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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