I'm no guitar tech, but the tension on the strings will be acting to pull that crack apart, it might have even been the tension over time which actually did it?
Just from a general woodwork perspective (from watchign people fix stuff, not actually doing much fixing myself) it doesn't look the easiest of repairs. Gluing it an clamping it probably won't work as you're going to struggle to get the glue on all the grains which have parted, and the string tension is going to be trying to pull the same faces apart again, and glue won't hold it together on a "pulling" plane, so it would just break again and then it's more of a mess to repair. They might have to chop the neck/ head off, stick some dowels in, in line with the head and glue it back together, maybe even a butterfly joint.
It is of course repairable though, and well worth doing as all the main part of the guitar is still in good nick I expect and Takamine's are decent.