1. Look closely at the picture. The coordinates of several points in your solution do not match what we see. If we assume that point A is on the coordinate plane yOz, then there should be A(0,6,2), B(-3,0,4), C(5*cos(Pi/3),0,5*sin(Pi/3))
2. Of course, if the coordinates of all points are known, then there is no problem in finding any angles. This can be done using geom3d package or in any other way. The problem is that the condition also contains 2 forces and this obviously should be taken into account in the solution.
3. To include these forces in the solution, I assumed that the OA rod is not rigidly fixed in the wall, but simply rests against it and at the same time can freely tilt to any side. I also assumed that the first coordinate of point A is unknown (it is not entirely clear from the figure whether point A lies in the plane yOz or is shifted to the side). Under these assumptions, we have 3 unknowns and 3 equations for finding them, relying on static equilibrium (see my solution for details).