It would be great to figure this out - have tried this on my desktop with a Radeon 7970 and another computer with a 6970 using a pile of different driver versions but always a black screen as soon as I hit full screen.
I have been going through EA support for 2 months now. They keep getting me to repair and reinstall the game, Windows, Origin and just about every other bit of software on my PC but it doesn't resolve anything. They have finally suggested I log an issue with AMD, appears their specialist support is out of ideas.
The only solution I have heard on forums that has had confirmation from a few users that works is to purchase 3rd party drivers from Tridef.