RS-SMO 2008 Problem 6

In a convex pentagon $ABCDE$ , let $\angle EAB = \angle ABC = 120^{\circ}$ , $\angle ADB = 30^{\circ}$ and $\angle CDE = 60^{\circ}$ . Let $AB = 1$ . Prove that the area of the pentagon is less than $\sqrt {3}$ .