Classical Mechanics Puzzler

Consider three consecutive rotations; a +90o about the x1 axis, followed by a +90o about the x'2 axis, and ending with a +90o about the x''3 axis. The sequence is shown below.

What two subsequent rotations (there are at least two sets) will bring the system back to its original state? Solve this problem without resorting to matrices. A set of three differently colors pencils will make the task easier.



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