# 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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