Second-order difference of a sine

Let $$f(x)=x\sin\left(\frac{\pi}{2x}\right),\quad x>0.$$ Then $$\lim_{h\to 0}\frac{1}{\pi^2 h^2}\bigl[3f(1)-2f(1+h)-f(1-2h)\bigr]$$ is equal to __________ (round off to 2 decimal places)