Let $f:R \to R$ be a twice differentiable function such that $(\sin x\cos y)(f(2x + 2y) - f(2x - 2y)) = (\cos x\sin y)(f(2x + 2y) + f(2x - 2y))$ , for all $x,y \in R$. If ${f^\prime }(0) = \frac{1}{2}$, then the value of $24{f^{''}}\left( {\frac{{5\pi }}{3}} \right)$ is :