Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be a twice differentiable function such that \((\operatorname{sinxcos} \mat…

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

[JEE Main 2025, 2 Apr (Shift 1)]