Trouble with a classic statics problem

[Candalite]

Homework Statement

You are given three weights and 3 pulleys. Each mass hangs below a single pulley, and the pulleys are all connected by strings. The middle weight is 3 kg, the other two are each 2 kg. There are two unknown angles at the central pulley, with respect to the horizontal such that the lines connecting to the other pulleys would form the hypotenuse of a right triangle.

Essentially it's this: http://forums.xkcd.com/viewtopic.php?f=18&t=45987 only the angles are unknown, and the masses are changed to what I have listed above.

I have to find the angles if the system is at static equilibrium.

Homework Equations

None

The Attempt at a Solution

I tried breaking it down into force components, but something isn't right.

I figured the tensions would be 2g, 2g, and 3g all told, and that I'd need the components for the "v" shaped lines. I ended up with 2gcos(theta)-3gcos(theta)+3gcos(theta)-2gcos(theta) for the sum of the x components, and 4gsin(theta)-3gsin(theta) for the y components, but this does not work out correctly. I am now completely lost, and have no idea how to properly set up the force diagram to solve the equation.

 

[Candalite]

I solved the problem. I remembered that tension in the system causes acceleration in a given direction if the force (in this case, just the mass) of the system is greater (or lesser) than the tension. So I found the equilibrium for that.