And also, when r=0 any theta will still indicate the same point.
This non-uniqueness of polar-coordinates is intrinsic unless you make very well-defined canonization rules which is one of the reasons why they're really not good for comparing point equality.
As this is something very seldom needed for the applications where polar coordinates makes sense, it's not a problem unless you really want it to be.
So basically tashirosgt: why do you think this non-uniqueness might be a problem?
Reductionist and proud of it.
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