”Determine

Consider the unit circle and the given equation:

$\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \sqrt{3}$

We know that $\tan(\theta) = \sqrt{3}$ when $\theta = \frac{\pi}{3} + k\pi$, where $k$ is an integer. In the interval $[0, 2\pi)$, we thus find:

$\theta = \frac{\pi}{3}$ and $\theta = \frac{4\pi}{3}$.

Therefore, the solutions are:

$\boxed{\frac{\pi}{3}, \frac{4\pi}{3}}$

To determine the angles for which $ an( heta) = sqrt{3}$, we recognize that

$ an( heta) = sqrt{3}$ corresponds to the reference angle $frac{pi}{3}$.

Thus, we can write:

$ heta = frac{pi}{3} + kpi$ for any integer $k$.

Within the interval $[0, 2pi)$, we evaluate:

$ heta = frac{pi}{3}$ when $k = 0$

and

$ heta = frac{4pi}{3}$ when $k = 1$.

Hence, the solutions in the given interval are:

$oxed{frac{pi}{3}, frac{4pi}{3}}$

Given $ an( heta) = sqrt{3}$, we know:

$ heta = frac{pi}{3} + kpi$.

In $[0, 2pi)$:

$ heta = frac{pi}{3}, frac{4pi}{3}$.

The angles are:

$oxed{frac{pi}{3}, frac{4pi}{3}}$

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