You answered your own question with your calculation. In 6 months the earth is on the other side of the Sun, so you need 180 degree difference for daytime to keep facing the sun at the same time.
The 56 minutes is for a full 360 degree spin on axis, but one day is not 360 degrees of spinning, it’s a little bit more given that the earth not only rotates it also translates within its orbit.
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