Theta III was the third planet in its system. The location of this planet in the Milky Way Galaxy, in the Alpha Quadrant near Babel, was depicted on a Federation star chart in 2293. (Star Trek VI: The Undiscovered Country, production art)
The location of Theta III in "The Explored Galaxy" star chart was depicted between the Tholian Assembly and Romulus. Both were identified in DS9: "Call to Arms" as being located in the Alpha Quadrant.