For whatever reason, I am having a complete brain block; I would like to reflect the arithmetic spiral $$ r=\frac{\theta}{2\pi} $$ about the polar axis. This should be possible? But I can't quite figure out how to go about it. The spiral crosses the polar axis at every integer value of $r$, so it seems to me that as $r$ increases after passing through $\theta=0$ at an integer, the angle needs to decrease from $2\pi$, rather than continue increasing as in the original function. I have a hard time finding examples online. I am looking for something like this:
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