Let \( f : \mathbb{R} \to \mathbb{R} \) 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 \( x, y \in \mathbb{R} \). If \( f'(0)=\frac{1}{2} \), then the value of \( 24\, f'\!\left(\frac{5\pi}{3}\right) \) is:
