Centroid Of A Tetrahedron

Geometry Level 4

If $$P(x,y,z)$$ is the centroid of the tetrahedron with vertices $$A(1,0,0), B(0,0,0), C(1,1,1)$$ and $$D(0,0,1)$$, then evaluate $$x+y+z$$.

Image Credit: Wikimedia Aldoaldoz.
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