Does θέατρο refer to theatre as an art, to theatre as the location one goes to, or both?
Both...... e.g. I am going to the theatre.......live theatre is expensive to stage /put on.
Isn't popular a predicative adjective? If so, then the sentence should be The theater/theatre is popular.
Popular theatre refers to a type of theatre, e.g. Music hall type comedy rather than Shakespeare. It does not mean that the theatre is popular. Hope that helps.