For what value of x does the function y = x + 2 cos x have a horizontal tangent line?

I said f'(x) = 1 + 0(cosx) + 2(-sinx) = 1 - 2sinx

So if the line is horizontal, f'(x) must = 0, so 0 = 1 - 2sinx --> sin x = 1/2

Now I am stuck. What value of x should I put? 30 degrees? pi divided by six?

???