Its not quite as obvious as you might think. Basically the screen is made up of pixels, and its impossible to aim between them, so all you need is enough DPI to not skip pixels as you move the mouse over them. For that you can work out how much DPI you need:
Its (screen width resolution x 4) / (inches for 360 turn) = minimum DPI needed to not skip pixels for 90 degree FOV. Whether it really matters if you do skip pixels is worth considering too, and really I don't think its a big deal.
EG if you have 1024 res and turn 360 in 11 inches (28 cm) you need 372 DPI. Setting your DPI over that won't make any positive difference. You don't put the DPI to max because you end up with poorer response from the mouse. You can get negative acceleration, skipping, and you can't move it as fast while getting perfect response from the mouse. This is why you won't find any top level FPS players using high DPI.
Since none of us are pro's tho, in the scheme of things it doesn't really matter, but if you want to get the most from the mouse then don't just put it to its max DPI, you're just downgrading its response for no actual gain.