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Degree is letter-like and not an operator
[Degree] is letter-like, not an operator,
Therefore, when we write 360° that is analogous to 2π (pun intended) it this interpreted as: 360 times "degree", and analogous to: 2 times "pi".
Note also that writing: [Degree] == Degree is valid, and this would not be the case if this symbol were not letterlike.
You're right, it should be a symbol, not an operator. I will batch this change along with a few others.