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Kevin Federline 's new book "You Thought You Knew" details his first fight with his ex Britney Spears ... and it's a doozy -- KF says he caught her cheating with a female dancer!

In an excerpt from his new book, obtained by USA Today , Kevin says the alleged incident happened during a wild night on tour in Amsterdam, back at the hotel. Getty

KF writes, "Britney and I went to our room, but shortly after, she said she’d be right back. At first, I didn’t think much of it. The hotel floor was ours; they had booked it out for the entire tour, so everyone’s rooms were nearby. But as time passed, I began to wonder what was taking so long."

KF continues ... "Eventually, I decided to check if everything was okay. I stepped into the hallway, our door still cracked, l

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