Verified answer

4sin(x/2) * cos(x/2) ≤ -1 

2sin(x)<=-1

sin(x)<=-1/2

sin(x)=-1/2

x=(-1)^n*arcsin(-1/2)+pi*n

(-1)^n*arcsin(-1/2)+pi*n <=x <= (-1)^(n+1)*arcsin(-1/2)+pi*n>