The Unit Circle and Circular Functions · Superchallenge problem

Define $t_1 = \dfrac{2\pi}{7}$, and for $n \ge 1$ let $t_{n+1}$ be $2t_n$ reduced into $[0, 2\pi)$ (subtract whatever whole number of full turns is needed). Find the smallest integer $n > 1$ for which $t_n = t_1$.