My left arm is paralyzed so tangled earphones is even more annoying for me to untangle than the average Joe.
I decided to cut two holes in the collar of the jacket I wear most often these days and a third hole next to the pocket I keep my phone in and attach the lead "permanently".
I poked an earphone through each collar hole and the 3.5mm jack poking out the pocket hole - remembering to leave enough slack to connect the lead before puting the phone in my pocket so I can turn the radio on.
Radio won't start until the lead is in as it becomes the aerial so if I kept the lead short and connected it after puting in my pocket I wouldn't be able to see to touch the screen..
I splodged a bit glue inside the holes to keep the three pieces of wire in place, I only had glue for hard plastic lying about so used that, it aint pretty but is hardly noticable.
Before I started I put the jacket on with the earphones in my ears and the cable behind my neck then took a look in the mirror to guesstimate where to make the holes.
The buds hang down inside my jacket so can't be seen when not in use, I can't feel them and they haven't tangled in several weeks of daily use.