Final answer:
Hamlet demonstrates the theme of loyalty and duty by requesting Rosencrantz and Guildenstern to be killed for their loyalty to Claudius.
Step-by-step explanation:
In the forged letter that Hamlet sends to the king of England regarding Rosencrantz and Guildenstern, he requests them to be killed due to their betrayal and misplaced loyalty in Claudius.
This demonstrates the theme of loyalty and duty as Hamlet believes that their loyalty to Claudius makes them unworthy of forgiveness and deserving of death.