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Calculus Level 5

\[\large \sum _{ n=0 }^{ \infty }{ \dfrac { 1 }{ n+1 } \sum _{ k=0 }^{ n }{ { (-1) }^{ k }\dbinom{n}{k}\ln { \left( \dfrac { 4k+3 }{ 4k+1 } \right) } } } =a\pi\]

If the above equation is true, find \(a\).

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