I had the tire valve core stuck strongly in side the valve because of over tightening which was not possible to take out and by this method you can force the broken core to turn open using screw driver with force
Just use a small torx like a T10 with the hole in the middle kind. But 1- put a penetrant lubricant first. then 2- blow some air in there before to blow off the dirt or corrosion out of the way. 3- Then the Torx after pressing it all the way in.
i hope by now it is solved. You need good screwdriver , (edges new )and you need to push hard while rotating and this will make open by friction force , i inserted in any possible gap