You can put this solution on YOUR website! Find all the solutions of the equation in the interval [0,2pi] cos 2 theta= 1-3 cos theta
***
cos(2x)=1-3cos(x)
2cos^2(x)-1=1-3cos(x)
2cos^2(x)+3cos(x)-2=0
(2cosx-1)(cosx+2)=0
..
2cosx-1=0
cosx=1/2
x=π/3,5π/3
or
cosx+2=0
cosx=2 (reject, -1 < cosx < 1)
(