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Re: In what situation don't we need to put "the" in front of first,second,third,etc.?
You could say 'a fourth day' here, because we don't know how long it will last, but 'its' is probably more common. If you know the length of something, then you wouldn't use the indefinite article:
It's the second day of the Easter holidays.
It's a second day of the Easter holidays.
In what situation don't we need to put "the" in front of first,second,third,etc.? 
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