You can be right and not angry.

For me, a big epiphany came through examining my intent while angry and whether the anger was helping or hindering that intent.

There are some cases where it can help, though might still not be the best tactic. It makes you more willing to use more force when doing something physical; but you are capable of that force with more control when not angry. And it can have social effects: intimidation, empathy, increased resistance, and trolling.

Empathy is really the only beneficial one, though it often involves patronization because it reduces you to a child throwing a tantrum, so it's a bit of a pathetic one.

Intimidation doesn't convince people, though they may appease you in the moment or even long term, but each time you do that, you're "cashing in" some of the relationship and possibly putting a target on your back if those you intimidate see any way of eliminating you as a threat.

And obviously increased resistance or trolling are the opposite of what you want to accomplish.

Once you've convinced yourself that anger doesn't help regardless of whether you're right or right to be angry, then it's a matter of reminding yourself about this when you feel anger flaring up instead of trying to justify it. Don't punish yourself about it, it's ok to feel anger even if unhelpful and getting more upset that you got upset is even more counterproductive.

It's not easy. You will probably even fail to control your anger sometimes and let your emotional side dictate that this time it's different or you just don't care this time. Nothing you can really do other than reflect honestly on it later, once the anger has passed.

You can also pause to examine your feelings in the moment of anger. What are you feeling right then? Why? Where do you want things to go from there? How could you get there? Is it really that important? Could you be the wrong one? Could it be a big miscommunication and you're actually arguing about two different things? Why is it so upsetting that someone feels differently from you? Why do you feel like it's your job to correct this?

Though one form of anger we should hold on to is indignant rage at living in a system designed to fuck us from multiple angles all at once.