Tau Day was first. specifically created as a day to promote tau over pi being taught in schools. (because 2 pi is always better than one.) (sorry. sorry. Couldn't resist.)
Tau isn't real, it's a social construct. Think about it: did you ever see tau in nature? "I have eaten tau apples" said no one ever. Face it: it's made up by humans and isn't real in any meaningful way
considering that pi is the ratio of a circle's circumference to it's diameter, where tau is the ratio of a circles circumference to it's radius, anywhere you see 2pi in nature, you're seeing tau, too.
Don't mind me. I just like making bad math puns; so 2pi will always be better than 1. (especially around my family... quite vociferous about which pie is best. Apple, btw.)
2pi is always what you see. I don't think there's a situation it's ever alone. It may look like it is sometimes, but that because it was divided by two already wherever the formula was derived from. Tau is the actual useful number, and 1/2 Tau somehow became mainstream
honestly I think I wanna write (2*pi) every time I need tau just to avoid confusing others. Maybe make it auto-subsitute or something. But many mechanical engineers have no idea why to use tau and use 2pi instead.
Just use 1/2 tau anytime you need pi instead. Eventually they'll learn.
Edit: actually, this'll never come up because tau usually alone and 2pi is used as a replacement and never alone. You never need just 1 pi, unless it was divided by 2 already.