Puzzle Angle formed by Stacked Squares

[@beautifulmindinpuzzles7716]

Calculations could be made simpler if we first rationalize the denominator of tan(alpha). We then see that tan(alpha)=tan(beta)=SQRT(2) - 1. Now use double-angle identity. I enjoyed your geometric solution. It is elegant. Geometric solutions are usually much shorter than trigonometric, algebraic or even methods of calculus.

[@UjjwalRane]

Thank you!