Just park it. Or sell it. Fixie's are dangerous, both to you and those around you, inefficient, and don't make you a better rider, quite the contrary. They will degrade your spin, not improve it. We had a fixie rider die here - couldn't stop and went right under a dump truck. And many other accidents. If you have issues, settle them on a race course.

None of this is true of a single-speed bike with a freewheel and two brakes, BTW. That can be a fine training tool for infrequent training use or commuting, where fewer parts may outweigh the disadvantages.