Calculating the required angle, theta.
Let it be a.
Let the side length of the 4 congruent squares be 1 unit each.
Therefore.
tanb = 1/3
b = atan(⅓)°
tanc = 1/(½)
c = atan(2)°
d = 180-c
d = (90+atan(½))°
Therefore;
a+b+d = 180
a = 180-atan(⅓)-(90+atan(½))
a = 90-atan(⅓)-atan(½)
a = (atan(2)-atan(⅓))°
a = 45°
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