First, we note that $\tan 75^\circ = \tan (45^\circ + 30^\circ)$.
Using the tangent addition formula, we have
\[\tan 75^\circ = \frac{\tan 45^\circ + \tan 30^\circ}{1 - \tan 45^\circ \tan 30^\circ}.\]
We know that $\tan 45^\circ = 1$ and $\tan 30^\circ = \frac{1}{\sqrt{3}}$,
so substituting these values gives us
\[\tan 75^\circ = \frac{1 + \frac{1}{\sqrt{3}}}{1 - 1 \cdot \frac{1}{\sqrt{3}}} = \frac{\sqrt{3} + 1}{\sqrt{3} - 1}.\]
To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator:
\[\tan 75^\circ = \frac{(\sqrt{3} + 1)(\sqrt{3} + 1)}{(\sqrt{3} - 1)(\sqrt{3} + 1)} = \frac{4 + 2\sqrt{3}}{2} = \boxed{2 + \sqrt{3}}.\]
The answer is: 2+\sqrt{3}
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
What is the value of tangent of 75 degrees?

### Answer:
