But, according to you, I do not understand the difference between a DC voltage and AC voltage.You are a marvelous engineer.
It that were true, I'd not be fit to be called an engineer. Let alone marvelous. Yet, that's the charge you are laying at my door.
From anyone with reasonable knowledge and experience of electrical circuits, I'd have been chagrined to have been so charged.
In this case, I just found it amusing.
I have provided ample information including real life oscilloscope measurements that support my point that Van and Vbn are mutually displaced by 180 degrees or pi radians if you prefer that measure. Using N as the reference point is entirely logical since that's the common point in residential supplies.
So, how about you now reciprocate with your measurements that show it to be different in any way shape or form.
As my late uncle was fond of saying, your move son.