J.F.
I know this will be hard to do, but ignore his outburst while he is sitting in time out. I see you have moved the chair out of sight, so just let him know what rule or guideline he broke, for instance 'we don't throw toys' and the consequence for throwing the toy is removal of the toy and sitting in time out for 2 minutes.
He is screaming and spitting and behaving this way because it gets attention. As long as he cannot hurt himself or anything else while in time out, it is perfectly acceptable to ignore him for those two minutes. After the time is up, go back to him and repeat again that he is not to throw the toy, and as long as he is not screaming or spitting any more, he can go play again. He'll learn quickly that the behavior is not getting him attention and he'll stop. It may take a few times of leaving him again in time out but unless he tantrums for 20 minutes, it won't be a big deal.