Sum of $3$ triangles' angles: Geometric proof of $\tan^{-1}1+\tan^{-1}\frac12+\tan^{-1}\frac13$

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3 square problem

In the given figure,3 squares are fitted together. Some lines are drawn. What is the value of $\alpha +\beta +\gamma$?

I just can derive alpha as 45 degree as it is an angle formed by diagonal of square. How to find the other two?

I have seen similar questions that were solved using trigonometry. I just want the process how to solve it by using only elementary geometry.

Also I saw another problem that answered its complements but I can't understand it