In my opinion, we should not consider gravity force (at least, we don't receive its mass to compute mg). Just calculate 2 force in the horizontal plane to find the 3rd force to make object is in equilibrium.
x-axis
\sumFx = 0
F1(cos30)+F2(cos75)+F3x = 0
225(0.866)+135(0.259)+F3x = 0
F3x =...