Question: Symbolic resolution of trigonometric equations system

Hello,

I would like to determine a closed form solution (=analytical solution) of the following trigonometric equations system.

TrigonometricSystem2.mw

The unknowns are :

ListAllUnknowns := [Psi(t), Theta[1](t), Theta[2](t), x[1](t), x[2](t), z[1](t), z[2](t)]

Do you have ideas so as to conduct the symbolic resolution of this trigonometric equations system ?

I have been told that the use of Grobner basis could be useful but I have never try this.

Thanks a lot for yours feedbacks.

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