Given $\cos x + \cos y + \cos z = \frac { 3 \sqrt { } 3 } { 2 }$ and $\sin x + \sin y + \sin z = \frac { 3 } { 2 }$ then show that $x = \frac { \pi } { 6 } + 2 k \pi , y = \frac { \pi } { 6 } + 2 \ell \pi , z = \frac { \pi } { 6 } + 2 m \pi$ for some $k , \ell , m \in \mathbf { Z }$.