I don't see any errors in this, I'd venture that you simply need to recheck the calculations, make sure you haven't stepped in the time honored pitfall of degrees/radians and suchlike, have the right angle for gamma and so on.
However, to nitpick a little, I'd make sure to be consistent with signs; in the figure, for example, the xcomponent of F is negative and the ycomp is positive, but it's flipped over in the equations. No biggie in a task like this, but it helps to be a perfectionist with details like that when things get more complicated!
