I have a simple C++ equation that I'm using to perform lens distortion correction.

$$y=\frac{\arctan(x)}{x}$$

where $x$ is in radians between 0.0 and 1.0.

I'm trying to come up with the inverse of this equation [get $x$ given $y$] but I've been unsuccessful. I got this far before my flabby math skills were exhausted:

$$xy = \arctan(x)$$
$$\tan(xy) = x.$$

I realize that this question sounds like a homework problem but trust me, I haven't had homework in several decades. I would appreciate pointers on where to look or even google terms.