Could you kindly suggest me ways to find out closed form solution of the following equation type:

$$\tan(nx)=k\tan(x),$$

where $n$ and $k$ are some positive real numbers (that excludes zero). I can solve it using series expansion, but that gives me only an approximate solution for $x$.

Thanks in advance.

PS: I am in engineering stream, but I usually don't need to solve problems that seems very tough to me, mostly just couple of additions/subtractions etc.