Area of an Inscribed Regular Dodecagon

Consider a regular dodecagon (a twelve-sided polygon) that is inscribed in a circle with a radius of 1 unit. To find the area of this dodecagon, we can use the formula:

$$ ext{Area} = 3 imes ext{side length}^2 imes ext{cotangent} \left( \frac{\pi}{n} \right) $$

where $n$ is the number of sides, and the side length can be calculated using:

$$ ext{Side length} = 2 \times r \times \sin\left( \frac{\pi}{n} \right) $$

For a dodecagon inscribed in a circle with radius $r = 1$, calculate its area.