Number of real values of `x in [0,4 pi]` for which `|sin x|+|sin x-1|+|sin x-3|+|sin x-4|=6` is:

If 0 le x le (pi)/(2) , then the number of value of x for which sin x - sin 2x + sin 3x = 0 , is

If 0<=x<(pi)/(2), then the number of values of x for which sin x-sin2x+sin3x=0, is

The number of real values of x satisfying the equation 3 sin^(-1)x +pi x-pi=0 is/are :

Number of integral values of 'a' for which the equation cos2x+3sin x+4sin^(2)x=a-3 has a real root is/are

Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy sin^(-1)((3x)/(5))+sin^(-1)((4x)/(5))=sin^(-1)x is equal to :