is it profitable to setmine vs 3bet from utg?

My first guess would be that it is

PRO:

The tighter his range is, the more implied odds you get when you git

+

for 100bb stacks:

if you OR 3x and he raised to 9x you only invest 9% of your stack while you will hit a set about 12% of the time

CON:

you are out of position and this makes it harder to inflate the potsize

there will be times that you hit your set but still lose the hand

It depends on their post-flop aggression and the size of the 3-bet relative to your stacks.

You will flop a set with a pocket pair 1 out of every 8 times. Therefore, to be profitable theoretically and satisfy the implied odds you could call if the 3-bet was less than 12.5% of your stacking stack.

However, as the opponent won't commit all of his chips when you hit a set everytime and you won't win in each situation with three of a kind you need to be playing with a narrower range. I recommend calling if the 3-bet is less than ~6% - guaranteeing you only need to stack him off 1 out every 20 times to be profitable. (+sometimes you are going to win with a PP without hitting a set)

yeah many people talk about how bad playing OOP is and generally i think this is taken to mean that it's hard to win pots. but actually it extends also to getting value, as lorenzoa has suggested. try being OOP with a monster.. your options are bet (but then you may only just get called), or check/raise. with check/raising you give the opportunity to check behind (so you fail to build a pot) and, if they do bet when you check, your check/raise is so strong they probably won't pay you off with a relatively weak hand. so for that reason i think it's difficult to say and it all depends on the villain.

i dont think that there are many people that are 3betting more than 6% against an UTG open
i think its hard win the pot witout hitting a set if he cbets more than half pot i rarely think you have odds to call