Sometimes, its better to adopt a complex way than a simpler one

Geometry Level 5

\[\sin(x)+\sin(y)+\sin(z)=0 \\ \cos(x)+\cos(y)+\cos(z)=0\]

Given that \(x,y,z\) are real numbers satisfying above two equations , evaluate:

\[\begin{align} &\tan^2(x)+\tan^2(y)+\tan^2(z) \\ - &\tan^2(x)\tan^2(y)-\tan^2(y)\tan^2(z)-\tan^2(x)\tan^2(z) \\ -&3\tan^2(x)\tan^2(y)\tan^2(z) = \ ? \end{align}\]


This problem is original.
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