ABCD is a square with side length of 2, rotated through 45 degrees so that the diagonal BD becomes horizontal. A circle of unknown radius is drawn through B and D as shown. Within the large circle two further circles are drawn, respectively above and below BD, and the maximum size they can be whilst staying within the large circle.

The region that lies within the large circle but outside of the two smaller circles is shaded.

What is the area of the shaded region?