It's Collateral Damage that has the Chopin in it, and Muse included it as a homage of sorts. Bellamy has included some Rachmaninov and Tchaikovsky in other songs before too (Space Dementia and Hoodoo).
It's always slightly disappointing when you find out artists have taken bits from other pieces of work. Something that the OP might sympathise with is that for about a year I thought Paul Gilbert wrote the long verse sequence in Scarified - he pinched the entire thing from Bach and didn't give any credit to him.
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