The Greeks were already an established culture in southern Italy whean Rome was created.
Because Rome and Greece's city-states in Italy were so close together,
Greece strongly influenced Rome in many different ways.
Rome's ideas on many things were borrowed from the Greeks, things ranging from gods to theatre construction.
The layout of the Roman theatre is very much like that of the Greek theatre.
They both have an orchastra pit, a backstage area, and seating arrangments.
Also, the ideas for plays were 'borrowed' from Greek plays.
The plots were basically the same only the characters' names were changed and some other minor things.
Even the rules on producing plays were similar to those in Greece.