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Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3...

Let `|{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0`, then the number of values of x satisfying the equation is

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