Tgα+tg2α-tg3α=-tgα*tg2α*tg3α
tgα-tg3α=sin(α-3α)/(cosα*cos3α)=-sin2α/(cosα*cos3α)
tgα+tg2α-tg3α=sin2α/cos2α-sin2α/(cosα*cos3α)=
=sin2α(1/cos2α-1/(cosα*cos3α))
1/cos2α-1/(cosα*cos3α)=(cosα*cos3α-cos2α)/(cosα*cos2α*cos3α)=(1/2*(cos2α+cos4α)-cos2α)/(cosα*cos2α*cos3α)=(cos4α-cos2α)/(2cosα*cos2α*cos3α)=(-2sin3αsinα)/(2cosα*cos2α*cos3α)=-tgα*(1/cos2α)*tg3α
sin2α(1/cos2α-1/(cosα*cos3α))=sin2α*(-tgα*(1/cos2α)*tg3α)=-tgα*tg2α*tg3α, ч.т.д.