2. Using geometric figures, the value of $\operatorname{tg} 75^{\circ}$ can be found as

保留源文本的换行和格式，直接输出翻译结果如下：

2. Using geometric figures, the value of $\operatorname{tg} 75^{\circ}$ can be found as
$2.2+\sqrt{3}$.
In the right triangle $\triangle ABC$, $\angle C = 90^{\circ}, \angle B = 75^{\circ}, \angle A = 15^{\circ}, BC = 1$. On the side $AC$: take a point $D$ such that $\angle ABD = 15^{\circ}$, then $\angle BDC = 30^{\circ}, \angle DBC = 60^{\circ}, AD = DB = 2 \cdot BC = 2, CD = BC \cdot \tan 60^{\circ} = \sqrt{3}$. Therefore, $\tan 75^{\circ} = \tan \angle ABC = \frac{AC}{BC} = \frac{AD + DC}{BC} = 2 + \sqrt{3}$.