Find the x intercepts of $f(x)=\tan\left(x\right)-\tan\left(4x\right)$

Question

I'm having serious trouble finding the x-intercepts of this funtion $$f(x)=\tan(x)-\tan(4x)$$ I'm unable to solve it for zero. What am I missing here?

Answer 1

Hint

$$\tan a =\tan b\iff a=k\pi +b$$

Answer 2

Simplify: $$f\left(x\right)=\tan\left(x\right)-\tan\left(4x\right)=\frac{\sin x\cos 4x-\sin 4x\cos x}{\cos x\cos 4x}=\cdots$$