Hands of the Clock....

The angle of the minute hand is \theta And the hour hand is \beta

Then, \beta -\frac{\theta}{12} is a multiple of 30 degrees...

in the same way if the hands are reversed, the same logic says that, \theta-\frac{\beta}{12} is a multiple of 30

adding, we get 11\frac{\theta+\beta}{12} must be a multiple of 30...

subtracing, we get 13\frac{\theta-\beta}{12} must be a multiple of 30...

I hope you can finish this from here! (If what I have done is not with mistakes)
I am lazy right now to finish it off