Love Circles

Geometry Level 4

The points \(A\), \(B\), \(C\), \(D\) are the centers of the circles as shown above. The circles \(A\) and \(B\) each have a radius of length 1 cm. and pass through each other's center. Similarly, the circles \(C\) and \(D\) each have a radius of length 3 cm. and also pass through each other's center, inscribing the smaller circles inside the overlapping portion.

What is the area of the pink section (in \(\text{cm}^{2}\))? Give your answer in the nearest 3 decimal places.

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