A geometry problem by Dexter Woo Teng KoonGeometry Level 5
The points \(A\),\(B\),\(C\) and \(D\) are the centers of the circles as shown above. The line \(EF\) is the tangent line to the 2 big circles. \(CA=AB=BD\). Line \(CD\) is parallel to line \(EF\).
If the area of the blue section is 1, find the area of the red section.
Give your answer in the nearest 3 decimal places.