Ok, so I took your hint, and found that angle that would yield the equilibrium position, aka forces balance, and accel = 0.
using that angle, I found the y position that would yielf equilibrium.
I labeled the mass in the middle as m1 and the masses on the outside as m2.
F = ma System m2...
I'm trying to figure out this problem too.
I think what you're supposed to realize here is that the tension forces are doing work on the three masses, but since your system is everything, work = 0, and so you have to express that as a potential energy... so in a sense, you're trying to find TPE...