External TV antenna grounded inside attic?
You should run a ground wire from the the mast grounding block, but I would not ground it to anything other than the grounding electrode conductor at the source. If you have a ground rod that is where I would connect it. If there is lightning, your mast could be subject to a strike and I would want it to go directly to ground and not through any other part of my system that could be upstream of some pieces of equipment that may be damaged. Use at least a solid #10 and make sure any radius has a nice long arch. 

The metal sheath in a coax is not a ground, it is a shield which drains off misc radio and electronic interference. So it needs to be grounded on one end and left open on the other. So if it has a coax block you can ground it there just make sure you are not grounded at the other end. You also need to make sure the the coax block is grounded to the mast.

Good Luck