Avoid what mistake?
The Law of Sines is always correct.
In your example, the angle A cannot be 60 degrees.
[Since the triangle is isosceles, with the base angles at 30 degrees each, then the 3rd angle, angle A, cannot be 60 degrees only.
sinA = sqrt(3) / 2.
Then A is not 60 degrees only.
Sine is positive in the 2nd quadrant too, so A = 120 degrees there.
Given the choice A=60deg or A=120deg, which one fits your triangle?