Don't know what that was all about... :?
But on a more serious note, that is a good question. And the only thing that is making me hesitate from painting the back of my acrylic tank. Did you paint yours or did you buy it that way? If you don't know what type of paint it is it makes it more difficult I guess. As far as I know the best way would be to LIGHTLY srape off the majority then sand the entire back with wet/dry sand paper. Starting with something like a 600 grit then moving to finer like 1200, then very fine 4000. Then you would need to polish it. Using something like the Novus polishing system, starting with #3 and working down to #1.
If you plan on painting it again, say a different color, it doesn't need to be that polished so the #3 alone would be the last step.
Hope that helps.