okay so just use it as an equation.
if 2sin0 + 3^(1/2) = 0
2 sin0 = - 3^(1/2)
then sin0 = (-3^ (1/2))/2
do sin^-1(-

)
= -1/3pi
we want it between 0 < x < 2pi
so add 2pi (equivalent to 360degrees)
= 5/3pi
and to find the second value, (2pi - 5/3pi) + pi = 4/3pi
answers are 5/3pi and 4/3pi