Idk if this belongs in Gameplay or Behavior, since it's technically a Gameplay tip on how to use the chat effectively but whatever.
First of all, don't mute them, that's the very first mistake. Just because you can't see the problem, it doesn't mean the problem doesn't exist. Having a tilted teammate makes the game basically 4.5 v 5 at that point.
Also, if they find out you muted them, it will only make them angrier.
Well, the second thing you need to do is to EXPECT NOTHING from your teammates. If you expect nothing from a person, you will never be dissapointed. Just pretend they are all bad from the very start. This is the best way not to tilt yourself, incase you are that type of person.
Third, and most important tip.
Whenever he types something in chat directed at you, it doesn't matter how bad it is. Something about your mother, wishing a disease upon you, calling you racial slurs. It doesn't matter one thing.
Just type in chat "uwu". And no, it's not a slur in some random obscure language or anything (well, not that I know of, at least). UwU or uwu is just that, UwU.
Your raging teammate dies? type uwu
Your raging teammate flames? type uwu
Your raging teammate does something amazing? type uwu, then follow it up with a gj or something if you want to, but there's no need to do so if you don't want to.
And here's the reason why it's so effective.
Eventually, the dude will stop moaning about you, not because you are playing any better but because he feels like it's absolutely pointless to do so since all you will write is uwu and he will start moaning about your Galio mid for dying for the 12th consecutive time.
And that's ok.
If Galio learning anything from the chat, he should now type uwu. And whenever he directs anything to him, he should now answer with uwu.
And it doesn't matter. Eventually all 4 of you will be typing uwu, he will just assume you are all premade, even if you are in a SoloQ game.
This will either untilt the dude, since he will see there is no point in arguing with uwu, or he will start flaming the enemy laners instead.
If he ever types uwu back, then you've done your job.
PS: doesn't work with rivens