Prove , if x is a rational number , x ≠ 0 then , tan(x) is not rational

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The discussion centers on proving that if x is a non-zero rational number, then tan(x) is not rational. Lambert originally proved this theorem, and participants are seeking the proof details. A reference to Laczkovich's simplification of Lambert's proof is mentioned, which can be found on Wikipedia. The conversation highlights the challenge of finding a comprehensive proof. Overall, the thread emphasizes the mathematical significance of the relationship between rational numbers and the tangent function.
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prove , if x is a rational number , x ≠ 0 then , tan(x) is not rational

this theorem was proved by a mathematician called Lambert ,
I search for the proof , anyone knows it ?!
 
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