Find exact values of x such that 2 since =-square root 3 where 0<x<2 pi

2 sinx = -√3

sinx = -√3/2
so the reference angle is x = π/3
sinx is negative in QiiI and QIV, so
x = π+π/3 or 2π-π/3
that is,
x = 4π/3 or 5π/3