For what values of x is the trigonometric equation tan(x − 180°) − sin(x − 180°) = 0, where 0 ≤ x < 360°, true?

Using the 180° shift identities, tan(x − 180°) = tan x and sin(x − 180°) = −sin x. The equation becomes tan x + sin x = 0, or sin x(1 + cos x)/cos x = 0, where tan x is defined. In the interval 0° ≤ x < 360°, this holds at x = 0° and x = 180°, so the answer is {0°, 180°}.

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