calculus - Numerical approximation by hand of arctan?

Is there any numerical method I can use by hand to solve an equation with $\arctan$?

I have for instance:
$$
2x\frac{180^\circ}{\pi}+\arctan(2x)=150^\circ
$$
Or in radians:

$$
2x+\arctan(2x)=\frac{5\pi}{6}
$$

Update:

With "by hand" I mean without a computer, just with pen, paper and a simple calculator.