#2/3sin^2x-cosx=1#
#2/3(1-cos^2x)-cosx=1# Pythagorean identity #sin^2x+cos^2x=1#
#2/3-(2cos^2x)/3-cosx=1# expand brackets
#2-2cos^2x-3cosx=3# multiply both sides by #3#
#-1-2cos^2x-3cosx=0# subtract 3 from both sides
#2cos^2x+3cosx+1=0# multiply both sides by #-1#
#(2cosx+1)(cosx+1)=0# factorise
#cosx=-1/2,-1#
#x=120, 180# for #[90,180]#