Let the sequence $\left\{ a _ { n } \right\} _ { n \geq 1 }$ be defined by $$a _ { n } = \tan ( n \theta )$$ where $\tan ( \theta ) = 2$. Show that for all $n , a _ { n }$ is a rational number which can be written with an odd denominator.
Let the sequence $\left\{ a _ { n } \right\} _ { n \geq 1 }$ be defined by
$$a _ { n } = \tan ( n \theta )$$
where $\tan ( \theta ) = 2$. Show that for all $n , a _ { n }$ is a rational number which can be written with an odd denominator.