어쩌라고 is used when a person got annoyed or for showing the person doesn't care about what others say, or when really don't know what to do next. And, it's not polite expression. You should use 어떻게 before a Korean verbs or clause, whereas '어쩌라고' can stand alone. The nuance of '어쩌라고' is a slang, and more informal than '어떻게 하면 됩니까?'