Two similar tiny balls of mass m are hung from silk threads of length L and carry equal charges q. The angle formed by the two strings is bisected by an imaginary line, forming angle θ. Assume that θ is so small that tan θ can be replaced by its approximate equal, sin θ. The distance between the two charged masses, at equilibrium, is x. Show that, for equilibrium,
x = ((q2L)/(2∏ε0mg))1/3
Clearly, Coulomb's Law is a vital piece of this problem, and other sources that I've checked suggest such things as the constancy of the ratio of the sides of a triangle divided by the sine of that side's opposite angle and combining the electric force and gravitational force into the components of the force of tension.
The Attempt at a Solution
Despite having a couple of ideas about how to start, I haven't made much progress. I noticed that there is an identical problem here (https://www.physicsforums.com/showthread.php?t=305517) that suggested the constant sine ratio rule, but I can't for the life of me get to the right answer. Any help would be appreciated.