All the problem betwen PI and TAU is comming of a bad definition of the notion of radian.
An angle is define like the SURFACE betwen too crossings lines, and NOT like an arc of circle.
So, if that, 360 degrees is equivalent to PI (PI*r2 , with r=1) and not to 2*PI.
With this definition of radian, we have the perfect eiPI=1 instead of eiPI=-1.
When I was yonger I have never liked this -1 but I didn't understood why.
That is the reason. A bad definition of the Radian.