solve for k (constant) in tankx =-1/root3

where k>0 has a solution of x=60 degrees

i did inverse tan(-1/root3) which gave me -30 degrees

so -30/k = 60 right?
-30/60 = -0.5
but the question said k>0 so i dont know what to do

ok well we know that $\tan(60k) = -\dfrac{1}{\sqrt{3}}$.

Indeed, arctan'ing both sides yields $60k = -30$. However, tan repeats itself every 180 degrees hence $-30 + 180 = 150$ is also a possible value for $60k$ to have.

The question isn't that great because there are infinitely many possible values of $k$ such that $\tan(60k) = -\dfrac{1}{\sqrt{3}}$ and they just say 'k>0' without much else.