You can either solve this via CSS OR Fullscreen API.
I think you can accomplish this by changing the css for the #document fragments, these are DOM1 specs and supported by all browsers, but about the styling, I'm not sure. The following solution is webkit specific.
You need just to write this code in your css:
2. Full screen API
If you want to accomplish it by Fullscreen API check below demo first:
As you can see a very simple demo showing HTML5 video in full screen, make sure you're using Chrome dev, webkit or firefox nightly.
For more detail you can check it here. Browsers may provide a user interface, but shouldn't provide a programmable one.