# Summing up factorials (3)

Calculus Level 5

$\sum_{ k=0 }^{ \infty }\sum_{ i=0 }^{ \infty } \dfrac{ { (-1) }^{ i+k } }{ \left( 2k+1 \right)!(2i)!(i+k+1) } = \sin^b(a)$ If the above equation is true for natural numbers $$a$$ and $$b$$. The find the value of $$a+b$$.

Note: Angles are measured in radian.

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