Best way (if any) to turn off 4G when screen is off for 5+ min and switch to 3G, then switch back?

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http://androidforums.com – Is there a good way to do this? I have automateit but I am not sure it is possible (maybe with tasker?). I would like to set an automatic rule that switches my phone from 4G to 3G (so that I still receive push notifications) after the screen has been off for a certain amount of time (5+ min), and automatically turn 4G back on when I turn the screen on again. Does anyone know of a way to do this? I am using Droid DNA with Android 4.1 and not rooted. Correct me if I'm wrong, but I don't believe that you root a DNA at this time. (General)