tan(x+π/4)+tan(x-π/4)
=(tanx+1)/(1-tanx)+(tanx-1)/(1+tanx)
=[(tanx+1)^2-(tanx-1)^2]/(1-tan^2x)
=4tanx/(1-tan^2x)
=2tan2x=2cotx,
——》tan2x=cotx=tan(π/2-x),
——》2x=kπ+π/2-x,
——》x=kπ/3+π/6.