Is there a way to reverse the effect of $a\tan2$?

I have a specific question about reversing $a\tan2$. (I am programmer, sorry for the jargon). I also use the $a\tan2$ function in my example, but I think everybody knows what it means.

Is there a way to reverse the transformed value to the start radial, without knowing the start radial? This is how codeflow should be

I have searched on the web (incl. stack) but I couldn't find any correct code. Also looked on Wikipedia, but it was overwhelming. My question is more a algebra question I think ;).

Let me know what you think!

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My guess at the meaning of the question. Suppose $t = -\mathrm{atan2}(2\cos\theta,(3/2)\sin\theta)$, where $\mathrm{atan2}$ is defined by $\mathrm{atan2}(x,y) = \arctan(y/x)$. Solve the equation for $\theta$ as a function of $t$. – GEdgar Jun 20 '11 at 16:37
If this guy is let loose bridges will collapse. – Christian Blatter Jul 20 '11 at 18:06

The normal inverse of atan2 is the tangent function-it takes in the angle given to atan2 and returns the ratio of $y$ to $x$. That's the best you will get as atan2 throws away the radius from the origin.