tan[a+b]= [tana+tanb]/(1-tanatab)
tan[a-b]= [tana-tanb]/(1+tanatab)
tan(x/2+π/4)-tan（π/4-x/2）
= [tan(x/2)+1]/[1-tan(x/2)] - [1-tan(x/2)]/[1+tan(x/2)]
= {[tan(x/2)+1]^2-[1-tan(x/2)]^2}/[1-tan^2(x/2)]
= 4tan(x/2)/[1-tan^2(x/2)]
= 4tan(x/2)cos^2(x/2)/[1-tan^2(x/2)]cos^2(x/2)
= 4sin(x/2)cos(x/2)/[cos^2(x/2) -sin^2(x/2)]
= 2sinx/cosx
= 2tanx