"-는데" sets up the situation and 어쩌다 asks what can be done about it — usually rhetorically, as a way of refusing responsibility. The makeup artist did it, so what do you want from me? I couldn't do that if I died, so what do you want? I keep eating more, what am I going to do? The other shape is 어쩔 수 없이, "having no choice": I really meant not to sleep but I dropped off anyway. Note that two of these lines contain 어쨌건 "anyway", a different word that just happens to start the same way.