Solve $x = \frac{1}{2}\tan(x)$ I did this using trial and error, but I was just wandering if there is an algebraic way of solving this?

I thought about double angle formula but that doesn't work properly does it?

I then tried writing it in the form $x \cdot 2 \cot(x) = 1$ but even then, I can't solve it properly by re-writing $\cot(x)$ because of the $x$ outside the brackets.

Anybody know how I would do this algebraically?
Of course, the roots are transcendantal numbers, which cannot be expressed in terms of a finite number of elementary functions. But they can be expressed on the forme of series :
It cannot be solved algebraically as it is a transcendental equation.