Final answer:
Hamlet speaks to Rosencrantz and Guildenstern about his disillusionment with the world, describing Denmark as a 'prison' and expressing his loss of joy, but does not divulge the full extent of his troubles or knowledge of the King's betrayal.
Step-by-step explanation:
When Rosencrantz and Guildenstern meet with Hamlet, they are unaware that Hamlet knows they have been sent by the King. Hamlet describes his problems to them by expressing a deep disillusionment with the world, but he does not grant them full insight into the depths of his melancholy or his knowledge of the King's treachery. Instead, Hamlet speaks to them in a roundabout fashion, hinting at his acute distress and sense of confinement in Denmark, which he describes as a 'prison.' He tells them that he has lost all joy and that Denmark is a weary, stale, flat, and unprofitable place to him.
However, the excerpts provided do not directly show the interaction between Hamlet, Rosencrantz, and Guildenstern discussing this matter; they mention other aspects of the play and critical interpretations of Hamlet's character.