Use the trig identity sin(2x) = sinxcosx + sinxcosx = 2sinxcosx

so sin(2x) = sqrt(3) * sin(x)

=> 2sinxcosx = sqrt(3)sinx

=> (2cosx)sinx = (sqrt(3))sinx .........i rewrote this so you would see the connection.

To maintain equality, 2cosx must be equal to sqrt(3), so the solution to our equation is the solution to 2cosx = sqrt(3)

=> cosx = sqrt(3)/2

=> x = pi/6