There are two ways to avoid getting your throwline tangled up in tree limbs: 1) Shoot it with higher accuracy, or 2) manipulate it while it's up there, in a way that doesn't get tangled.

shoot it more accurately

have a safe way to "reset" the shot

"After each throw, let the weight return to the ground, untie it and retrieve line alone. Today's prediction: you’ll learn that advice the hard way."

manipulate it without getting tangled