The solutions of the trigonometric equation are x₁ = π / 6 and x₂ = 5π / 3.
How to solve a trigonometric equation on a given interval
In this problem we find a trigonometric equation which has to be simplified and solved for x to find the family of solutions within the given interval:
csc x · tan x = 2√3 / 3
(1 / sin x) · (sin x / cos x) = 2√3 / 3
1 / cos x = 2√3 / 3
cos x = 3 / 2√3
cos x = √3 / 2
Then, by inverse trigonometric functions:
x₁ = π / 6, x₂ = 5π / 3
To learn more on trigonometric equations: https://brainly.com/question/22624805
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