Just a pentagon!

In the pentagon $ABCDE$ , $AB=\sqrt{2}$ , $BC=CD$ , $\angle ABE=45^{\circ}$ and $\angle DBE=30^{\circ}$ . Compute the area of the pentagon if a circle of radius 1 can be circumscribed about this pentagon.

The area is in the form $\frac{a+\sqrt{b}}{c}$ , where $a, b,$ and $c$ are positive integers. Find the value of $a+b+c$ .