What is the exact context of using this phrase? Is a positive connotation attached to it or a negative one?
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The common version of this expression is "get into a groove," which means to get used to a routine, to get settled into a comfortable pace doing something, to hit one's stride.
It would normally have a positive connotation in American English ("I got into a groove about the middle of the race"), but you could use it to imply that you are unable to get out of the routine, and in British English to "be in a groove" may more often relate to boredom.
See these definitions:
The expression "get into the groove", on the other hand, can mean to have fun or to get with the times, usually in a positive way. This phrase is probably a bit dated (1985 Madonna, anyone?). "The groove" is a reference to musical rhythm, probably from the physical groove in a record. This discussion sums it up pretty well:
To "get into the groove" is generally a positive thing; its etymology comes from dance and live music, and it implies finding the beat and rhythm of music being played and moving to it. That usage in turn most likely stemmed from the use of vinyl records up until the mid 1990s; vinyl EPs/LPs have a literal "groove" with the analog sound wave pattern moulded into it and picked up by a needle; "get into the groove" may thus have been used literally to mean "put the record on the player and drop the needle in the groove".
It is now used figuratively to refer to finding and following any sort of rhythm, or finding one's place in a group. It is roughly synonymous with "go with the flow" or "find your rhythm".
In the groove (or into the groove) is an informal phrase used to mean "in (or into) the groove informal performing consistently well or confidently."
It could also mean "indulging in relaxed and spontaneous enjoyment, especially dancing."