An unusual sum

Calculus Level 4

\[\large{\displaystyle \sum _{ r=1 }^{ 2014 }{ \psi \left( \frac { r }{ 2015 } \right) \sin { \left( \frac { 2\pi r }{ 2015 } \right) } } =-\frac{A}{B}\pi}\]

Given that the summation above is equal to \( -\dfrac AB \pi\), where \(A\) and \(B\) are coprime positive integers, and \(\psi (x)\) denote the digamma function. Find the value of \(A+B\),

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