Help with a complex pulley problem

[stonecoldgen]

Homework Statement

The problem is based in the diagram (the jpg attached).

All pulleys are ideal pulleys, and the hanging surface is massless. the problem states that the guy with mass m pulls each string with a force F, and asks to solve the value of F in terms of m and g. Since the pulleys are ideal I know that the forces on the ends are both F, as marked in the diagram, but I don't know what are the values of T1 and T2 (note:T1=T2). If anyone could please help I would appreciate it.

ƩF=0=-mg+2F+F+F+T1+T2

 

[Simon Bridge]

isolate the pulley associated with T1 and draw a free body diagram for it.