엊그제 literally means 어제(yesterday) + 그저께(the day before yesterday), and it's used only if the correctness doesn't matter.
You should use 그저께, if you want to be specific on "the day before yesterday".
2017年11月17日
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엊그제 means "a couple of/ a few days ago", while 그저께 means "day before yesterday".
I hope this helps!