TanX+Tan2X+TanX.Tan2X =1

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Solution

tanx+tan2x+tanx.tan2x=1
tanx+tan2x = 1 - tanx.tan2x
(tanx+tan2x)/(1 - tanx.tan2x) = 1
tan3x = 1
3x = π/4 + nπ, n = 0, ±1, ±2, ...

x = π/12 + nπ/3
= π/12(1 + 4n)

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