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CZ-SK-MO 2006 Problem 6

    Find all real solutions (x,y,z)(x,y,z) of the system of equations: {tan⁡2x+2cot⁡22y=1tan⁡2y+2cot⁡22z=1tan⁡2z+2cot⁡22x=1\begin{cases} \tan ^2x+2\cot^22y=1 \tan^2y+2\cot^22z=1 \tan^2z+2\cot^22x=1 \end{cases}

    Dataset text AI-MO AoPS. Quoted with source.

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