This can be written: 2sin^2xcosx=cosx because sin2x=2sinxcosx and we can divide through by 7.
So cosx=0 is a solution, and x=n(pi) radians or 180n degrees, where n is an integer.
Also, we can now divide through by cosx: sin^2x=1/2 so sinx=sqrt(2)/2 and x=(pi)/4 radians or 45 degrees.
The cyclic solution is 45+360n, 135+360n or (pi)/4+2n(pi), 3(pi)/4+2n(pi).