First minor hurdle: Mma treats backslashes in strings as escapes. But even after doubling them all, I still get "Could not parse [BLAH] as Mathematica input". A bit of experimenting suggests that Mma doesn't like \cdot, so I removed those. I took out the explicit linebreaks at the same time.

Now Mma is able to parse the TeX. So far as I can tell from a quick glance, it's understood it OK. Unfortunately, I've had no success in getting it to plot it. RegionPlot[...==0...] produces nothing. ContourPlot[...==0,...] produces nothing. Without the ==0, unsurprisingly, no contour Mma chooses to draw looks at all appropriate. The trouble is that (1) the function is varying so damn fast in the relevant region and (2) those zero contours are all "valley-bottoms", and there's not much way for Mma to know they're there at all. Even giving unreasonably large values for WorkingPrecision,PlotPoints and MaxRecursion doesn't help, unless you consider running the Mathematica kernel out of memory "helping".