`Sinx+Sin2x+Sin3x+Sin4x =0.` Find sum of roots that lying in `[0,2pi]`

If 2sin^(2)x+3sin x+1=0 then the sum of all the values of x lying in [0,2 pi] is (k pi)/(2) where k is

If 2sin^(2)x+3sin x+1=0 then the sum of all the values of x lying in [0,2 pi] is (k pi)/(2) where k=

If sin5x+sin3x+sin x=0. then the value of x other than 0 lying between 0<=x<=(pi)/(2) is

If |(sinx,sin2x,sin3x),(sin2x,sin3x,sinx),(sin3x,sinx,sin2x)|=0 then the number of values of x in interval [0,2pi] is

If sin5x+sin3x+sin x=0, then the value of x other than 0 lying between 0<=x<=(pi)/(2) is

sin x+2sin2x=3+sin3x0<=x<=2 pi has

In the interval (0,2 pi) , sum of all the roots of the equation sin(pi log_(3) (1/x)) = 0 is

int_(0)^(pi//2)sinx sin2x sin3x sin 4x dx=