Why at the end of Hamlet, Shakespeare refers at least four times to theater.
Using words such as "stage" and "put on". At the end, Fortinbras orders Hamlet's body to be placed on a "stage" twice. Then he refers to Hamlet's potential as "put on", which is another theatrical term.
Does it have to do anything with Rome and Juliet? I remember, Shakespeare uses "Let's put on Rome and Juliet"
The use of stage terms in the closing scene of Shakespeare's Hamlet very directly reflects a line from another Shakespeare play, but it's not Romeo and Juliet, it's As You Like It:
All the world's a stage...
Existence in Hamlet is like being on a stage--everybody's acting:
- Hamlet pretends to be mad.
- Claudius pretends to be honest and just, and pretends to care about Hamlet. He toasts him in the closing scene, when he is really trying to get him to drink the poison in the cup.
- Polonius, Ophelia, Ros. and Guil. all spy on Hamlet, pretending to be his friend, or more, while actually trying to get information out of him.
- The 1 Player pretends to care about Hecuba.
- Laertes pretends to forgive Hamlet, and treats him with respect, while he is in the process of trying to kill him.
All the world, existence, is a stage in the play.
Specifically, though, the theatrical terms you mention all have literal meanings in the lines you cite. For instance, "put on," when used by Fortinbras, simply means that if Hamlet would have been "put on" the throne, he would have proved most royal.
Figuratively, I suggest the terms suggest the idea that life is a stage, and everyone acts like this or that; everyone wears masks, plays roles. This is much stronger in Hamlet than is any suggestion of drawing attention to the fact that those putting on the play are actors. That is not central to this play, as it might be in Romeo and Juliet. Why? Because there's no chorus in Hamlet. Shakespeare had matured and was past the use of a chorus by the time he wrote Hamlet. He does not go out of his way to draw attention to the actors themselves, instead of the characters, in Hamlet.
I don't know about the connection to Romeo and Juliet, but there are many moments of the players or the chorus making it clear that their actions and everything else is understandably a part of a dramatic production.
If you look at Hamlet and the fact that there is a play within the play that is meant to bring out some of the issues currently producing the stench of "something rotten in the state of Denmark," the emphasis on staging and the play at the end of the action makes sense. If you consider Horatio's role as the one who will remain to tell Hamlet's story to the world, it again makes sense that some acknowledgment is made of the fact that the whole point of the play is to tell some story, in this case the one of Prince Hamlet.
The awareness in some sense, of the players, that they are in fact putting on a play fits with the fact that there are asides and soliloquys where Hamlet debates the issues that are present in the play. You can certainly make the argument that Shakespeare was making these players somewhat self aware of the fact that they are in fact players acting a part.