Task C4 version 21, reshebnik termehu Targ SM 1982

Solution of the C4 version 21 of Reshebnik on theoretical mechanics to the training manual Targ SM 1982.
Task C4 - to balance the spatial system of convergent forces.
Check the condition of the task C4 (Pages 25-27 Manuals Targ SM 1982):
Six weightless rods are connected at their ends hinged to each other in the two nodes and attached the other ends (also hinged) to the fixed supports A, B, C, the D (Figure S4.0 -. S4.9, Table C4.). The rods and nodes (nodes located in the tops of H, K, L or M cuboid) not shown and must be shown to solve problems in the data table. The site, which is listed first in each column of the table, a force F = 200 N; at the second node Q = applied force of 100 N. The force P forms with the positive directions of the coordinate axes x, y, z angles equal respectively α1 = 45 °, β1 = 60 °, γ1 = 60 °, and the power Q - angle α2 = 60 °, β2 = 45 °, γ2 = 60 °; direction of axes x, y, z for all figures are shown in Fig. S4.0.
Facets of the box parallel to the xy plane, - squares. Diagonals other lateral faces form an angle with the xy plane φ = 60 °, and the diagonal of the parallelepiped forming with this plane an angle θ = 51 °. Determine the forces in the rods.