Light switch wiring rats nest
This is a long slog, but it's straightforward. You have at least 7 cables.  The 3-way circuit and 3 switches can explain 5 of them at most.  

Don't unhook anything else. 

First, since you know there's one of a pair of 3-way switches here, Romex Cable #1, the /3 cable, can be positively identified as being for the 3-way circuit, since nothing else would work.  Fortunately we see its white wire join four other black wires, so white is being used to send always-hot to the other 3-way.  The other two wires (red and black) are travelers.  Mark them both with yellow tape so they can be easily recognized as travelers.  The common terminal on this 3-way switch must therefore go to the lamp.  That would be a cable where the white joins other whites, but the black is in search of this 3-way switch.  It looks like you have that exact situation on Romex #4.  

Romex cable #7 and #6 both have their hots going to a wire-nut (the one with the 3-way white).  That means one of them is supply, and the other one takes power onward to another point-of-use. It doesn't really matter which one is which. 

Romex cable #5 black seems to go to the smart switch on the left, so presumably it goes to the lamp controlled by the left smart switch. 

Romex Cables #2 and #3 have their neutrals going into the big bundle. Then, I can't quite tell, but it appears they have their hots joined together with a pigtail, which is then nutted onto the left smart switch.   If this smart switch controls 2 lights, then this explains all the cables.  

If the two installed switches are working, then all you have left to do is wire the /3 switch, yellows to brass, and solo black wire from #4 to black.