Let \(f:R\to R\) be a twice differentiable function such that \((\mathrm{sinxcosy})(f(2\mathrm{x}+2\mathrm{y})-f(2\mathr…

Let \(f:R\to R\) be a twice differentiable function such that

\((\mathrm{sinxcosy})(f(2\mathrm{x}+2\mathrm{y})-f(2\mathrm{x}-2\mathrm{y}))\)\(=(\mathrm{cosxsiny})(f(2\mathrm{x}+2\mathrm{y})+f(2\mathrm{x}-2\mathrm{y}))\),

for all \(\mathrm{x},\mathrm{y}\in R\).If \({f}^{'}(0)=\frac{1}{2}\), then the value of \(24{f}^{''}\left(\frac{5\pi }{3}\right)\)is:

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