Couple of thoughts.
I had one child (oldest) who had tantrums. Not to that extent, but still ..
I used to leave the room. I didn't even say anything other than "well, I don't feel like sitting here listening to this..." and up I'd get and go to the next room. At that age, they are fine .. I'd still check in out of the corner of my eye (always could see him), but I did not give him attention - I took it away. I never got upset, or angry, or raised my voice.
Or I'd say "when you calm down, then mommy will want to spend time with you again, and then we can play a game.." or something like that.
It didn't take long. He would realize he was all alone in the room crying, and as soon as he looked around and saw no one was there, he'd look for me. If he came into my room and started up, I would just repeat "Oh I'd rather spend time with a quiet little boy and do something fun".
It worked like a charm for us. It was just a stage we went through here. It was around the time we had another baby. I'd scoop up the baby and take him with me and say "oh too loud ... we're going to go in this room where it's quieter. You can join us when you are ready to be quiet". And then I'd thank him for being quieter when he came in to join us. I'd give him a hug.
You may want to run it past your doctor, in case his distress could be caused by a medical problem.
Mine if they were overtired, over stimulated, or over hungry always were worse. So I used to think of it more as what can I do to bring him back to a happy place - snack, quiet down time, hugs, his blankie ...
If it's just you he's doing this for, I would say you need to change your approach on how you deal with it. Time outs never worked for me (I know they do for a lot of people) for me though, removing myself as audience and not even giving him any attention for the tantrum was far more effective.
Good luck - hope it's just a phase.