Inverse trig

Geometry Level pending

If \(\sin^{-1} x +\sin^{-1} y + \sin^{-1} z = \dfrac {3\pi}2 \), then

\[\arcsin \left( \dfrac{2017 x^{2017} - 2016x^{2016}}{2015x^{2015}-2017x^{2017}}\right) = \frac{a\pi}{b} \]

where \(a\) and \(b\) are coprime integers. Find \(|a + b|\).

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