This truss rod had been stripped at the nut. In my experience, this is usually this is the result of using an under-sized allen key and rounding out the inside of the nut. In some cases you could replace the nut, or if it’s welded on, grind a slot into the existing nut and manage with a slot screwdriver from then on.
In the case of this guitar neither was possible and the truss rod was set in a state of excessive relief, meaning it was curved back and every note would buzz for the rest of it’s life. The truss rod needed replacing entirely or the guitar would always be unplayable.
The Takamine’s truss rod nut is actually encased by a sleeve which makes grinding a slot in it pretty much impossible. That is what I tried to do initially before I understood the design of these Asian-made rods. They are unlike the American-made 2-way rods most custom builders like myself use.