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If x + y + z = xyz, then prove that (2x)...

If x + y + z = xyz, then prove that `(2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2))`.

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Verified by Experts

`x+y+z = xyz`
Let `x = tanA, y = tanB, z = tanC`
Then,
`tanA+tanB+tanC = tanAtanBtanC`
It implies that,
`A+B+C = npi`
`=>2A+2B+2C = 2npi`
`:. tan2A+tan2B+tan2C = tan2Atan2Btan2C`
...
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