Solving high order trigonometric equation

For 0 less than or equal to x which is less than 2pi, solve

What can I do about that horrible power?

Student X

This probably needs to be solved by inspection rather than brute force expansion. 

Both the LHS and RHS share the same periodicity, in fact the equation can only hold if both sides yield an integer value. It might take a while for you to convince yourself of this. 

The broad solution set would actually be (2k+1) pi , where k is any chosen integer value. But since the question has specified a permissible range for x, there shall only be one solution, which is x=pi.  

Hope this helps. Peace.

Best Regards,

Mr Koh