Expected area of a random circular triangle

Consider a circle $C$ with unit radius and center at $A=(0,0)$. Let $B=(1,0)$. Suppose $\Theta\sim\mathrm{U}(0,\pi)$ and $D=(\cos\Theta,\sin\Theta)$. Note that the angle $\angle DAB=\Theta$. Then the expected area of the triangle $ABD$ is