[tex]\it a+b+c=\pi \Rightarrow a=\pi-(b+c) \Rightarrow tga=tg[\pi-(b+c)] \Rightarrow tga=-tg(b+c) \Rightarrow\\ \\ \\ tga=-\dfrac{tgb+tgc}{1-tgbtgc} \Rightarrow tgb+tgc=tga(tgbtgc-1) \Rightarrow tgb+tgc=tgatgbtgc-tga|_{+tga}\\ \\ \\ \Rightarrow tga+tgb+tgc=tgatgbtgc[/tex]
