The key to fish having trouble is to do the right thing. Doing the wrong thing can be worse than nothing at all. Fish are actually much tougher than we give them credit for, on the whole. Meaning: if you continually give the fish clean water to swim in, they can heal on their own with no other intervention on your part.
In other words... water changes. Lots of them and large ones. The more clean water the fish has to swim in the better able to cope with the problem. (This isn't the case in all situations, but in a situation where fins need to heal, that seems to be the safest route for all the fish. Medications can sometimes do as much harm as good. Some fish are very sensitive to them. And sometimes we use the wrong medications for a certain problem.) I would confirm the problem from someone with more experience with bettas (try that section, I'm sure you will get some very good advice).
Other questions to be prepared to answer:
Is this fish being picked on by the platies? (I know bettas are supposed to be these tough fish, but they really aren't. In fact, many faster swimming fish will nip at their long fins, and there really isn't much the betta can do about it. They just aren't very good swimmers.)
How is your flow rate in that tank? (Bettas prefer slow moving water, not fast moving water. You might need to redirect the output of your filter to cut down on the current in the tank.)
Are there any sharp edges the fish could snag a fin on in the tank?
ANOTHER THOUGHT JUST OCCURED TO ME:
Another option would be to completely change out the water in tank 3, and place the betta in that tank all alone. Tank 3 would be cycled sufficiently for one fish, and you wouldn't have to worry about him getting picked on. You also wouldn't have to worry about medicating all the other fish just because of the trouble with the betta. Having a hospital/quarantine tank is a great option to have. Fortunately, you do have an empty tank with a functioning filter that you could put him into. If I were going to be doing this, the best thing to do for him would be to isolate him.
Empty tank 3 completely. Pour a few gallons of water from Tank 1 into Tank 3. Then move the betta over. Slowly refill with temp matched dechlorinated water. Keep the flow rate of the filter low so that the betta doesn't have to struggle swimming. Feed only as much as necessary. (Speaking of feeding, what are you feeding the betta?)