Show that, if there exist $a \in \mathbb { R }$ and $t _ { 0 } \in \mathbb { R } ^ { * }$ such that $X ( \Omega ) \subset a + \frac { 2 \pi } { t _ { 0 } } \mathbb { Z }$, then $\left| \phi _ { X } \left( t _ { 0 } \right) \right| = 1$.
Show that, if there exist $a \in \mathbb { R }$ and $t _ { 0 } \in \mathbb { R } ^ { * }$ such that $X ( \Omega ) \subset a + \frac { 2 \pi } { t _ { 0 } } \mathbb { Z }$, then $\left| \phi _ { X } \left( t _ { 0 } \right) \right| = 1$.