What can I do to convince you that including an additional (2 PI)/N or N/(2 PI) factor into every single angle calculation you will ever do is a complete waste of time?
At the very least, you could take out the arbitrary N.
100 gradians is 0.25 rotations, or PI/2 radians. 30 degrees is 1/12 rotations, or PI/6 radians. There is no advantage whatsoever in multiplying everything by an arbitrary scaling factor that is not based on PI (or TAU).
The arbitrary factor of 400 (or 360), is simply not helpful for machine calculations.