Let $\theta _ { 1 } , \theta _ { 2 } , \ldots , \theta _ { 13 }$ be real numbers and let $A$ be the average of the complex numbers $e ^ { i \theta _ { 1 } } , e ^ { i \theta _ { 2 } } \ldots , e ^ { i \theta _ { 13 } }$, where $i = \sqrt { - 1 }$. As the values of $\theta$'s vary over all 13-tuples of real numbers, find (i) the maximum value attained by $| A |$, (ii) the minimum value attained by $| A |$.