On August 9, 1996, about 1213 central daylight time, a Cessna 172, N5291E, was substantially damaged after a loss of control and collision with trees while taxiing at Nashville International Airport, in Nashville, Tennessee. The private pilot was not injured in the accident. The airplane was operated by the pilot under the provisions of Title 14 CFR Part 91, and visual flight rules. Visual meteorological conditions existed at the time, and no flight plan had been filed for the personal flight. The flight was originating at the time of the accident. The pilot stated that he was taxiing out to the runway and lost effective braking on the right main landing gear brake. The airplane veered left. He released brake pressure to stay on the taxiway, exited the end of the taxiway, and rolled down a hill. The airplane hit several small trees before coming to a complete stop. An inspector examined the airplane's brake system and reported that no measurable hydraulic fluid was found in the master cylinder. He also reported that the brake fluid line that connects to the right caliper did not have a fresh leak but appeared to have a leak at one time. Residual fluid around the connection to the caliper was dark and sticky. According to the pilot's report of the accident, the airplane had operated 1.7 hours since the last annual inspection which was accomplished about one month prior to the accident.