AGP really?

Geometry Level 4

\[\large{f( x ) =\sin( x ) +\dfrac { 1 }{ 3 } \sin ( 3x )+\dfrac { 1 }{ { 3 }^{ 2 } } \sin( 5x )+\ldots }\]

Define \(f(x)\) as of above such that \(f\left( \dfrac { \pi }{ 3 } \right) =\dfrac { A\sqrt { B } }{ C } \) where \(A,C\) are co prime integers and \(B\) is square free.

Evaluate the value of \(A+B+C\) as your answer.

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