Properties of Triangle: JEE Main 2021 Mathematics question

Let ABCD be a square of side of unit length. Let a circle C₁ centered at A with unit radius is drawn. Another circle C₂ which touches C₁ and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C₂ meet the side AB at E. If the length of EB is $\alpha$ + ${\sqrt 3 }$ $\beta$, where $\alpha$, $\beta$ are integers, then $\alpha$ + $\beta$ is equal to ____________.