It's possible to get 2 of them from another Secret Room, but chasing that elusive 3rd is, shall we say, challenging. I don't remember where I got the 3rd, so I decided to think laterally when I got to the bridge where you need them, in case I fail to find that 3rd one in another playthrough.
Friends, my experiment worked. I offer it to those who need it.
Spoiler: show