어쩌자고

what do you expect to happen?

→ 어쩌다
어쩌자 how come, what happened + 고 And
verb Rare #27,531
what do you expect to happen? Often used rhetorically to express frustration or ask what someone expects you to do.
KO: 그걸 나한테 말해서 어쩌자고?
EN: What do you expect me to do with that information?
Conjugation of 어쩌다

어쩌자고 그래

What were you thinking?

— Night in Paradise (2020)

그래서 어쩌자고?

So what should we do?

— 저수지의 개들 (1992)

말해서 어쩌자고

What do you expect to accomplish by saying that?

— A Moment to Remember (2004)