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The general solution of the equation tanx + tan( x + pi/3 ) + tan (x + 2pi/3 ) =3
tanx + tanx + tanπ/3/1 - tanx tanπ/3 + tanx + tan2π/3/1 - tanx tan2π/3 = 3tanx + tanx + √3/1 - tanx √3 + tanx - √3/1 + tanx √3 = 3tan x ( 1+ √3 tanx) ( tanx + √3) + ( 1- √3 tanx) ( tanx - √3)/ (1+√3tanx) (1 - √3 tanx) = 3tanx + √3 + tanx + √3 tan^2x + 3tanx + tanx -√3 -√3 tan^2x + 3tanx/1 - 3t^2 = 3tanx + 8 tanx/1 - 3tan^2x = 39tanx - 3tan^3x/ 1-cos 3tan^2x = 33tan3x = 3tan3x = 13x = nπ + π/4x = nπ/3 + π/12
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