Question

( tan (A+B)=(tan A+tan B)(1-tan A cdot tan B) )
( begin{aligned} A & tan x+frac{tan x+tan pi}{1-tan x tan pi / 3}+frac{tan x+tan ^{2} pi / 3}{2 pi / 3}=3 end{aligned} )
set tans be ( t )
( sqrt{2} )
( x+frac{t+sqrt{3}}{1-t sqrt{3}}+frac{t-sqrt{3}}{1+t sqrt{3}}=3 )
take Lom and
( -3 t-3 t^{3} )
( frac{1}{1-3 t^{2}}=81 quad ) tenmon
( Rightarrow )
( tan 3 x=1 )
( Rightarrow 3 x=n pi+pi / 4 )
( x>frac{n pi}{3}+frac{pi}{12} )

# 13. The general solution of the equation tanx + tan (x + ) + tan (x + 2) = 3 is n 7 + -, nel nel ,ne nel 12

Solution