# It's kinda weird summation

Calculus Level 5

$\large \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1} \sin(k)}{k^3}$

If the above sum can be represented as $$\dfrac{\pi^a - b}{c}$$ for positive integers $$a$$, $$b$$ and $$c$$, find the value of $$a+b+c$$.

Clarification: Angles are measured in radians.

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