Find all solutions of the equation in the interval [0, 2π)

Question

Find all solutions of the equation in the interval [0, 2π)

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Write your answer in radians in terms of π

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If there is more than one solution, separate them with commas.

Answer 1

First, solving for the cotangent gives us cotθ = -√3/3. This means we need to find which angles this corresponds to. So for the reference angle, we know that an the angle θ=π/3 gives us the cotangent of +√3/3. Then the negative cotangent values occur in the second and fourth quadrants because the x and y coordinates have opposite signs. This means that we'd apply that reference angle of π/3 in each of those quadrants. That would make the angles θ= π-π/3 = 2π/3 and θ = 2π-π/3 = 5π/3. These are the two angles that give that satisfy the equation.

Answer 2