\[\large \int _{ 0 }^{ \pi /2 }{ \dfrac { { x }^{ 2 } }{ \sin { x } } \, dx } =A\pi G-\dfrac { B }{ C } \zeta (D)\]

If the equation above holds true for positive integers \(A,B,C\) and \(D\), with \(B,C\) coprime, find \(A+B+C+D\).

**Notations**:

\(G\) denotes the Catalan's constant, \(\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916 \).

\(\zeta(\cdot) \) denotes the Riemann zeta function.

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