The number of solutions of the equation sin3⁡xcos⁡x+sin2⁡xcos2⁡x+sin⁡xcos3⁡x=1 in the interval 0,2π is/are

sin3⁡xcos⁡x+sin2⁡xcos2⁡x+sin⁡xcos3⁡x=1or  sin⁡xcos⁡xsin2⁡x+sin⁡xcos⁡x+cos2⁡x=or  sin⁡2x21+sin⁡2x2=1or  sin⁡2x(2+sin⁡2x)=4or  sin2⁡2x+2sin⁡2x−4=0or  sin⁡2x=−2±4+162=−1±5This is not possible since  −1≤sin⁡2x≤1Hence, the given equation has no solution.