[QUE/ME-02003]

Show that the rotation matrix for rotation by an angle \(\pi/3\) about the direction \((1,1,1)\) as the axis of rotation is given by \begin{equation} R = \frac{1}{3}\begin{pmatrix} 2 & 2 & -1\\ -1& 2 & 2 \\2 & -1 & 2 \end{pmatrix}     \end{equation}