Vectors in Space · Hard problem

A tetrahedron has one vertex at the origin $O$; two other vertices are $A=(2,0,0)$ and $B=(0,2,0)$; the fourth vertex $C$ lies on the ray from the origin in the direction $(1,1,1)$, so $C = m(1,1,1)$ for some positive real number $m$. Find the positive value of $m$ for which tetrahedron $OABC$ has volume $4$.