You don't need a third gate valve. Do this
1. Drain the black tank
2. Close the black tank drain valve
3. Hold the drain hose above the level of the tanks. I usually just fling it over my shoulder.
4. Open both valves. This allows the gray tank water to back flush the black tank, removing any stuff from the gate valve
5. Close the gray tank drain valve
6. Drop the hose and allow the black tank to drain.
You can repeat steps 3-6 as many times as you want, but once will do it.
Finish up by draining the rest of the gray tank and rinsing the hose.