Jfet,
There are many tricks to keeping dropper tags from tangling, however, 3 of the best are:
1, Use a thicker leader(if presentation permits!)...I learned this stillwater fishing... 2x, 3x, or 4x, tangles WAY less than 5 or 6x (also different brands of leader material twist less)
2, Put the heaviest fly on the point when you are first learning to cast Euro nymphing rigs.
3, Tie the dropper using a triple surgeons(the lower tag) (make it about 4-8 inches in length) and put a half hitch in the dropper tag before you tie the dropper fly on. ---NOTE: if conditions require that you must fish 5-7x, than perhaps skip the half hitch, as it might possibly weaken the knot's breaking strength...
there are other tips and/or factors that help you avoid tangles(like pronating your cast a little) but try these three first
cheers
Pete