break of day vs break of the day

break of day and break of the day both are nouns.

Word	Noun	Adjective	Verb	Adverb
break of day	Yes	No	No	No
break of the day	Yes	No	No	No

As nouns, break of day and break of the day are synonyms defined as:

Other synonyms of break of day include aurora, cockcrow, dawn, dawning, daybreak, dayspring, first light, morning, sunrise, sunup.

break of day (noun)	break of the day (noun)
the first light of day	the first light of day