Given:

1. Use the following identity:

This way,

2. Clear tan(x) :
![\begin{gathered} 2+3\tan ^2(x)=3 \\ \rightarrow3\tan ^2(x)=1 \\ \rightarrow\tan ^2(x)=(1)/(3)\rightarrow\tan (x)=\pm\frac{1}{\sqrt[]{3}} \\ \rightarrow\tan (x)=\pm\frac{\sqrt[]{3}}{3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/hdtegfqsi0dht5ll5x65dm889fbk2bkyrm.png)
Now we know the value of the tangent of the angle we're looking for.
Tan(x) is positive for angles between 0° and 90°, and for angles between 180° and 270°. Knowing this, we need the angles in those intervals that have the tangent we've just calculated. This way, we get that.

Tan(x) is negative for angles between 90° and 180°, and for angles between 270° and 360°. Knowing this, we need the angles in those intervals that have the tangent we've just calculated. This way, we get that.

Therefore, the solutions are:

Note:
