A joining so deep that the parts can no longer be described separately. What happens to one is a fact about both.
English tangle, of disputed origin, most often traced to a Scandinavian source, prefixed with en- (into); a joining so thorough the parts can no longer be pulled apart cleanly.
Its own history is as tangled as what it names: tangle is of disputed origin, most often traced to a source for a knot pulled too tight to pick apart by hand. What is entangled shares that fate, pulling at one strand only moves the other, because by now there are no separate strands left to pull.