What themes are reinforced by the presentation of the Murder of Gonzago?

There are several ideas embodied in the play-within-a-play that
occurs in Act 3 in Hamlet.  The first that comes to mind is guilt.
The "Murder of Gonzago" is designed to "catch the conscience of the king.   Upon viewing the
play, Claudius reveals his guilt in killing his brother.  Claudius' conscience is indeed pricked,
and he attempts to atone for his crime through prayer.  The second theme might be
revenge.  In the play that Hamlet authored, the nephew to the king
is the one who kills the Player-king, not his brother.  Within the play is Hamlet's threat to
kill Claudius.  The next idea is the acting motif.  Everyone in the
play is playing a part--Hamlet plays the part of an insane man; Ophelia stages the returning of
Hamlet's tokens, Claudius plays the part of a concerned step-father; Guildenstern and Rosencrantz
act the part of concerned friends while being on the king's payroll.  No one is who they seem to
be--with the possible exception of Horatio.  The play-within-a-play is an extension and
reflection of the acting that those in the Danish court are involved with.  Lastly, the
spying motif is suggested.  Hamlet is spying on Claudius to
determine his guilt as he is watching the play. This is only one of many instances of spying that
occur in the play.  This motif relates to the ideas of trust and
betrayal.