How does Cassandra's speech in Agamemnon (before she enters the doors) add to the themes of the play?
It is impossible not to feel pity for Cassandra. Not only is she cursed with being able to see the future but having her predictions ignored by those around her, but she also is completely aware that her return to the homeland of Agamemnon spells not only his doom but also her own doom and her death. She herself has been fully aware of the fickleness of human fortune thanks to how she moved from being the lover of Apollo to being cursed, and so her final words as she goes into the doors of the palace to her doom pick up on this central theme of the capricious nature of fate and how human fortune is in no way dependable:
Alas for human fortune! When prosperous, a mere shadow can overturn it; if misfortune strikes, the dash of a wet sponge blots out the drawing.
This speech of course equally applies to Agamemnon as well as herself; remember that he is returning victorious from Troy having defeated the forced of Priam. However, little does he know or suspect the massive reversal of fortune that awaits him at his wife's hands. Even though he is "prosperous," it can be easily overturned, and his glory and fame can be easily blotted out by a "wet sponge." Note the way that Cassandra uses an implied metaphor to show how ephemeral and impermanent are status, power and fame. Her final speech therefore clearlyd develops the theme of fortune and how humans can experience massive reversals in their lives, even when they think they are most successful.