Answer:
120°
Explanation:
It is convenient to evaluate the expression 3tan²(x) for each of the given angles and see which give 1 or 3 as a result. The result for 120° is 9, so that angle will not be a solution to this equation.
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Solutions will be angles that make the factors zero. The first factor is zero when ...
... tan²(x) = 1/3
... x = arctan(±√(1/3)) = ±30° + k·180° for some integer k
Here, the angles of interest are 30°, 150°.
The second factor is zero when ...
... tan²(x) = 1
... x = arctan(±1) = ±45° +k·180° for some integer k
Here, the angles of interest are 225°, 315°.
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Comment on the solution set
The list of all solutions in the range 0–360° will include ...
... {30°, 45°, 135°, 150°, 210°, 225°, 315°, 330°}
