Three angles

A puzzle recently posted in Enigmatic Code,  Enigma 1329: Height of ignorance, reminded me of a related puzzle:  For three squares laid side by side as shown in the diagram, prove that  α = β + γ

Clearly  α = 45⁰. The obvious approach is to use multiple angle formulae, but there is a more elegant geometrical solution.

Click here to see the geometrical solution
The solution of this puzzle can be used to solve Enigma 1329.

There is also a simple solution using complex numbers which consists of 17 symbols: 

$(3+i)(2+i) = 5(1+i)$

Does this count as a haiku?