Making your web app toggle back and forth between full screen mode is a simple enough task as long as you do some feature testing. You can also use this handy function which will step through the 4 different feature tests:
This code is based off of documentation found here on MDN. I personally am using this code on my Big It! (a small web app that simply shows user entered text as big as possible). Feel free to use this function in any of your projects.