The title says it all, how do you say "speak one's piece" in Spanish?
 Speak your piece means "state your opinion or view".
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There is a debate if the correct phrase is "Speak one's piece" or "Speak one's peace". I have no intentions to go into details here, so I'm going to assume they are equivalent, or otherwise as explained here.
Decir todo lo que se tiene que decir.
The example the book gives is:
He spoke his piece. Dijo todo lo que quería decir.
It references someone's need to say something. I agree with the book, it would just translate to "decir lo que se tiene que decir" or "decir lo que se quiere decir".