For most of Act 3 in Shakepeare's Hamlet, the prevalent theme is duplicity.
In Scene 1, Claudius shows his propensity for deceit as he arranges for everyone put Ophelia to leave so that he and Polonius (who is hidden) can hear details from her seemingly private conversation with Hamlet. They hope the conversation will prove whether or not Hamlet is crazy:
For we have closely sent for Hamlet hither,
That he, as 'twere by accident, may here
Her father and myself, lawful espials,
Will so bestow ourselves that, seeing unseen,
We may of their encounter frankly judge
And gather by him, as he is behaved,
If't be the affliction of his love or no,
That thus he suffers for. (33-41)
Hamlet's use of duplicity is seen as he provides the text for the The Mousetrap to be performed by the players. He has written for them lines that, when performed, will likely force Claudius to admit his guilt in the murder of Old Hamlet.
In Scene 2 of this act, Claudius asks if the play will be offensive. Hamlet responds that it only "touches" the guilty. Hamlet tells the King:
Your Majesty...we that
have free souls, it touches us not. (230-231)
In another instance of deceit, Rosencrantz and Guildenstern are supposed to be Hamlet's friends, but they have sold their loyalty to Hamlet's stepfather. They have no concern for Hamlet; they wish only to further themselves in the King's service. Hamlet describes their intent to trick him to reveal his thoughts—noting that like an instrument, they plan to "play him," expecting him to make the "sounds" they want to hear:
Why, look you now, how unworthy a thing you make
of me! You would play upon me; you would seem to know
my stops; you would pluck out the heart of my mystery;
you would sound me from my lowest note to the top of my
compass; and there is much music, excellent voice, in
this little organ, yet cannot you make it speak. 'Sblood,
do you think I am easier to be played on than a pipe? (348-354)
They try to control him like they would a musical instrument, but he will not be taken advantage of or tricked.
Polonius is the prime example of deceitfulness in this act. In Scene 3, he decides to eavesdrop on the conversation because Gertrude and Hamlet, claiming that women cannot be objective about their their children and are thus unreliable. It is, of course, this deceitful plan that will lead to Polonius's death.
My lord, he's going to his mother's closet.
Behind the arras I'll convey myself,
To hear the process...
And, as you said, and wisely was it said,
'tis meet that some more audience than a mother,
Since nature makes them partial, should o'erhear
The speech, of vantage. (28-34)
The final scene in Act 3 further explores Polonius's death and the relationship between Hamlet and his mother. Most of this scene deals with the tragic results of deception.