Lines and both pass through the origin and make first-quadrant angles of and radians, respectively, with the positive x-axis. For any line , the transformation produces another line as follows: is reflected in , and the resulting line is reflected in . Let and . Given that is the line , find the smallest positive integer for which .
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email email@example.com.