Constructing A Crescent Moon

Geometry Level 1

Semicircle \(ADB\) with diameter 6 is rotated \(60^\circ\) anticlockwise at the point \(A\) to form another semicircle \(AEC\) with diameter \(AC\). If the area of the shaded region can be expressed as \(k\pi \), find \(k\).

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