Sum up the powered sines

Calculus Level 4

limnr=1n21rsin(2017r2n2)\large \lim_{n\to \infty} \sum_{r=1}^{n^2} \frac 1r \sin \left(\frac{2017 r^2}{n^2}\right)

If the value of the limit above is aπb\dfrac{a \pi}{b}, where aa and bb are coprime positive integers, then what is a+b?a + b?

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