Answer
The solutions are $0.4636$ and $3.6052$.
Work Step by Step
Add $1$ to both sides of the equation to obtain:
$2\tan{x} = 1$
Divide $2$ to both sides of the equation to obtain:
$\dfrac{2\tan{x}}{2}=\dfrac{1}{2}
\\\tan{x} = \frac{1}{2}
\\x=\tan^{-1}{(\frac{1}{2})}
\\x=0.463647609
\\x\approx 0.4636$
The period of the tangent function is $\pi$.
This means that $0.4636+\pi\approx 3.6052$, which is still within the interval $[0, 2\pi)$, is also a solution.
Therefore, the solutions are $0.4636$ and $3.6052$.
