System of tan equations

Geometry Level 4

\[\large{\begin{cases} x+y+z=3\pi/4 \\ \tan( x)+\tan (y)+\tan (z)=5 \\ \tan (x)\tan (y) \tan( z)=1 \\ \end{cases} }\]

\(x,y,z\) are real numbers satisfying the system of equations above Find the value of \(\tan^3( x) + \tan^3( y) +\tan^3 (z )\).

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