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You're right! Now I understand why it doesn't work. y = Sqrt[1-e^2] z = Sqrt[1-f^2] In addition e, f are elements of (-1,1). Now it should work, I've forgot that I made all formulas for this assumptions (and I didn't know how...
Also, the way you have Solve written here, it will look for Complex solutions for d, e, and f. I'm guessing you don't that?. If that's the case, you would begin by using ComplexExpand to separate the equations in their real and complex components and...