If 0≤x≤2π then the number of solutions of 3(sin⁡x+cos⁡x)−2sin3⁡x+cos3⁡x=8 is

The given equation is    3(sin⁡x+cos⁡x)−2(sin⁡x+cos⁡x)(1−sin⁡xcos⁡x)=8 or     (sin⁡x+cos⁡x)[3−2+2sin⁡xcos⁡x]=8 or     (sin⁡x+cos⁡x)sin2⁡x+cos2⁡x+2sin⁡xcos⁡x=8 or     (sin⁡x+cos⁡x)3=8 or     sin⁡x+cos⁡x=2or  sinx, cosx= 1, which is not possible. Hence, the given equation has no solution.