Final answer:
To solve the trigonometric equation tan²x + tan x + √3 tan x = √3, we simplify and factor it, before finding the values of x. If the equation seems too complex algebraically, a graphing calculator can be used to approximate the solutions.
Step-by-step explanation:
The student's question involves solving a trigonometric equation. The equation provided is tan²x + tan x + √3 tan x = √3, where the goal is to find the value of x. This can be tackled by rearranging the equation and then finding the roots of the resultant equation. The provided information seems to be either irrelevant or possibly typos from other mathematical contexts, and hence, does not directly contribute to answering this specific question. We would instead simplify the given equation, maybe factor it, and look for ways to solve it without the quadratic formula as it might result in a polynomial of degree higher than two. It's noteworthy that a graphing calculator can be a very effective tool to approximately find the roots (or zeroes) of trigonometric equations that may not be easily solvable by algebraic means.