Question 970967
{{{cos(2x)+cos(x)-1=0}}}
{{{2cos^2(x)-1+cos(x)-1=0}}}
{{{2cos^2(x)+cos(x)-2=0}}}


{{{cos(x)=(-1+- sqrt(1-4*2*(-2)))/4}}}


{{{cos(x)=(-1+- sqrt(9))/4}}}


{{{cos(x)=(-1+- 3)/4}}}


{{{cos(x)=-1}}}  or {{{cos(x)=1/2}}}
Notice where x points to on the unit circle for these cosines.
pi/3, 3pi/3, 5pi/3, and then as you continue to rotate in increments of to maintain those, you see difference of 2pi/3 each time.
... next value for x would be  7pi/3.


...as you keep on thinking on this, notice that x will be ODD increments of pi/3.  Now observe that your numerator for x IS AN ODD NUMBER.