Right Isosceles

Geometry Level 4

Given an isosceles right triangle $ABC$ , such that:

${AB=AC=1, \quad \angle BAC = \dfrac{\pi}2}$

Let $D$ be a point inside the triangle such that:

${\angle ADB = \dfrac{\pi}2, \quad \angle ABD = \angle BCD}$

Find the area of $\triangle ABD$ .