Doom 3 has a port called "Dhewm 3". Get that.
You should just be able to drop it into your Doom 3 folder, or just make a new folder if you want something cleaner. You'll need the game data from Doom3 patched to 1.3.1 (Not BFG edition). If you have it on steam, you already have it fully patched.
Specifically you need the files PAK000 through PAK008 from the "base" folder, and for Ressurection of Evil you need PAK000 and PAK001 from the "d3xp" folder.
Then for coop get the "Libre Coop" mod. Find the clovr server in the browser, or connect at clovr.xyz.
Widescreen seems to work great in single player, but not in multiplayer. There might be an ini or cfg fix for this that I'm not aware of.