Vectors in Space · Challenge problem

The tetrahedron $OABC$ has volume $3$. Points $P, Q, R$ are defined by $\overrightarrow{OP} = \overrightarrow{OA} + 2\,\overrightarrow{OB}$, $\overrightarrow{OQ} = \overrightarrow{OB} + 2\,\overrightarrow{OC}$ and $\overrightarrow{OR} = \overrightarrow{OC} + 2\,\overrightarrow{OA}$. Find the volume of the tetrahedron $OPQR$.