Let \(C_0,C_1,C_2....\) , denote the binomial coefficients \(^nC_0,^nC_1,^nC_2...\) so on.

It can be proved that,

\((C_1-C_3+C_5-C_7+\cdots) = a^{\frac{n}{b}} \sin(\dfrac{n\pi}{c})\).

Then find \(a+b+c\).

**Details and Assumption**

- \(a,b,c\) are positive integers.
- \(a\) and \(b\) have their minimum possible value.

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