Tgx+ctgx+tg3x+ctg3x=?

Tgx+tg3x+ctgx+ctg 3x=tgx+tg3x + (tgx+tg3x) / tgxtg3x = (tgx+tg3x) (tgxtg3x+1) / tgxtg3x = (sin (x+3x) / cosxcos3x) * (sinx sin3x+cosx cos3x) * cosx cos3x/sinx sin3x=sin4x*cos2x/sinx sin3x=1/2 * (sin2x+sin3x) / (1/2 * (cos2x - cos4x)) = sin (5x/2) cos (-x/2) / - sin3x sin (-x) = sin 5x/2 cos x/2 / sin3xsinx