The number of values of x between 0 and 2π such that the equation sinx+sin2x+sin3x=cosx+cos2x+cos3x must be
(sin3x+sinx)+sin2x=(cos3x+cosx)+cos2x
⇒2sin2xcosx+sin2x=2cos2xcosx+cos2x
⇒sin2x(2cosx+1)−cos2x(2cosx+1)=0
⇒(2cosx+1)(sin2x−cos2x)=0
⇒cosx=−12, tan2x=1
∴x=2π3, 4π3 or π8, 5π8, 9π8, 13π8