sin(7x) = sqrt(-3)/2
sin (7x) = -sqrt (3) / 2
Note
sin (7x ) = -sqrt (3) / 2 when either
7x = 4 pi / 3 + 2pi*n or 7x = 5 pi/ 3 + 2pi *n where n is an integer
Dividing both by 7, then
x = 4 pi / 21 + (2pi/7)n or x = 5 pi/ 21 + (2p/7)n where n is an integer