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Consider the set S = {x ∈ (-π, π): x ≠ 0, ±π/2}. What is the total sum of all unique solutions to the equation √3 sec x + csc x + 2(tan x - cot x) = 0 within the set S?

1. -7π/9
2. 7π/9
3. 0
4. 5π/9

Correct answer: 0

Solution

The equation is solved for x within the given domain. After simplifying the trigonometric terms and solving, it is found that the sum of all unique solutions is 0.

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