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∑k=1∞(−1)k+1sin(k)k3\large \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1} \sin(k)}{k^3}k=1∑∞k3(−1)k+1sin(k)
If the above sum can be represented as πa−bc\dfrac{\pi^a - b}{c}cπa−b for positive integers aaa, bbb and ccc, find the value of a+b+ca+b+ca+b+c.
Clarification: Angles are measured in radians.
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