Don't dare to try..... again

I have cut the square in 4 smaller, 2x2 squares(area 4). The larger circles have radius 1, so the area is pi. The smaller circle has radius $\frac{2\sqrt{2}-2}{2} = \sqrt{2}-1.$ . Now 1/4th of the green area equals:

$\frac{4-\pi}{4} - \frac{(\sqrt{2}-1) ^2\pi}{4} = 0.0789...$ .

So the total green area is 4 x 0.0789... = 0.319.