Solve the following trigonometric equation:

$$
\sin 2 x+3 \sin x=2 \tan x .
$$
Our equation can also be written as:

$$
2 \sin x \cos x + 3 \sin x = 2 \frac{\sin x}{\cos x}
$$

from which

$$
\sin x = 0 \text{ and } x = k \cdot 180^{\circ}
$$

and

$$
2 \cos ^{2} x + 3 \cos x - 2 = 0
$$

from which

$$
\cos x = \frac{1}{2}
$$

thus

$$
x = \pm 60^{\circ} + k \cdot 360^{\circ}
$$

(Hermann Szóllós, Esztergom.)