Another tip that you want to do which you just saw me doing is, nylon has a memory, and when you uncoil it you have all these coils which is very annoying but you can easily take the coils out of the leader.
All you have to do is pull it between your hands and stretch it. Stretch it, grab another piece, stretch it, grab another piece, stretch it. Obviously you get close to the tippet you get a little bit more gentle and you stretch it all the way to the end, and then you will have most of the coils out of your leader.
They sell some things called leader straighteners and some people sell them and usually it's just a piece of rubber or inner tube. The problem with leader straighteners is sometimes they heat up the leaders too much and they change the molecular structure and they could weaken it. So the easiest way to do it is don't worry about having an extra leader straightener hanging from your fishing vest or your pack, just stretch it with your hands. It's the best and easiest way to do it.