Answer
The solution set is $\{\varnothing\}$
Work Step by Step
$$\tan^2x+3=0$$ over interval $[0,2\pi)$
1) Consider the equation:
$$\tan^2x+3=0$$
$$\tan^2x=-3$$
We know that $A^2\ge0$ for $\forall A\in R$. As a result, $\tan^2x\ge0$ for $\forall x\in [0,2\pi)$
Therefore, as $-3\lt0$, there are no values of $x\in[0,2\pi)$ that $\tan^2x=-3$
In other words, the solution set of this equation is $\{\varnothing\}$
