In Claudius's soliloquy, we learn that Claudius did actually kill his brother. In his soliloquy, Claudius talks about his crime, and he says that it "bears the mark of Cain" who also killed his brother. Although we had been suspicious of Claudius throughout the story, this is the moment when our doubts are confirmed. We also learn that Claudius is extremely guilty about his actions, but that he believes that time and God's mercy will eventually help him overcome this feeling of guilt.
Claudius in his soliloquy is sitting down on his knees and confessing to the God that he has killed his brother. He admits his guilt and says that his act is unforgivable which shows that he is guilty.
A soliloquy is an act of speaking out loud one's feelings and expressions regardless the presence of people around. Soliloquy is mainly acted in a play when an artist plays a solo scene expressing his feelings as if no one is listening.
In the Act iii, scene 3, Claudius is accepting his guilt that he killed his brother, and this scene is a Claudius Soliloquy because it pretended as if no one is listening to Claudius.
There Act iii, scene 3 of Claudius's soliloquy shows that Claudius was guilty and was burdened with the murder of his brother.
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