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 \(\triangle ABD\).