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tan^(2)x tan^(2)3x tan4x=tan^(2)x-tan^(2...

tan^(2)x tan^(2)3x tan4x=tan^(2)x-tan^(2)3x+tan4x

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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