Targ S.M. 1989 C3 variant 15

Six weightless rods are hingedly connected at their ends to each other in two nodes and attached at their other ends to fixed supports A; B; C; D. The force P=200N is applied to the first node, and Q=200N to the second. The force forms with the positive directions of the x coordinate axes; y; z angles are equal to α₁, respectively; β₁; γ₁; and force Q - angles: α₂; β₂; γ₂ . The faces of the parallelepiped parallel to the XY plane are squares; the diagonals of the side faces form an angle φ=60⁰ with the XY plane; and the diagonal of the parallelepiped forms θ=51⁰ with this plane. Determine the forces in the rods.