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Calculate the average value of the following functions over the region $R$.

$$f(x,y) = 2\sin x \sin y; \quad R=\{(x,y): 0\leq x \leq \pi, 0\leq y\leq \pi\}$$

$\cfrac{1}{\pi^2}$

$\cfrac{8}{\pi^2}$

$0$

$1$

None of the above