mathematical non linear equation

i will need a solution from one mathematical non linear equation. I will need a solution for determination of values for few angles. So, we have Three Cartesian coordinate systemsOne is always static. The other two coordinate systems can rotate in circle and to move up and down and righ - left. Whether will be possible to be deteminate the angle between X axis and Y′ axis and also between X′ axis and Y axis ? Also, the angle between X axis with the normal line on the reference horizontal line and the angle between X′ axis with the normal line on the reference horizontal line from the first cartesian system? I am enclosing few photos. The first is from the initial position and the second is one example after moving of the both coordinative system independently. Photo 1, the link is: [login to view URL] The initial position are: C 1 is static always. C 2 (10,0) in reference to C1 (z1,z2) C 3 (-10,0) in referecen to C1 (z1,z2) angle ζ = 0 degrees angle ε = 0 degrees angles: α, β,γ, and δ are 90 degrees. Photo 2 (as one example) after moving of the both xoordiantive systems (CC2 and C3) in reference to C1 - the link is [login to view URL] C1 is static always. C2 values can be from (-1 to - 40) in reference to Z1 axis and from (0 to 40 and 0 to -40) in reference to Z 2 axis. C3 values can be from (1 to 40) in reference to Z1 axis and from (0 to 40 and 0 to -40) in reference to Z 2 axis. Also X can rotate from 0 to 180 degrees and from 0 to -180 in reference to Z1 axis (that is angle ζ ). So, the values of the angle ζ can be from -180 to 180) And X' can rotate from 0 to 180 degreesand from 0 to -180 in reference to Z1 axis (that is angle ε ). So, the values of the angle ε can be from -180 to 180) Probably we should give the input for: ζ, ε, C2 (z1,z2) and C3 (z1,z2) and then the values of the angles α, β,γ, and δ to be calculated. Thanks for your time and your help.