tan θ = −√3 for θ ∈ [0, 3π]

The given equation is tan θ = -√3.

The tangent function is negative in the second and fourth quadrants.

Step 1: Identify the reference angle.

The reference angle for tan θ = √3 is π/3 or 60 degrees.

Step 2: Determine the angles.

Since the tangent function is negative, we need to find the angles in the second and fourth quadrants.

In the second quadrant, the angle is π - π/3 = 2π/3.

In the fourth quadrant, the angle is 2π - π/3 = 5π/3.

Step 3: Find the angles in the given interval [0, 3π].

The angles in the given interval are 2π/3, 5π/3, 2π/3 + 2π = 8π/3, and 5π/3 + 2π = 11π/3.

So, the solutions to the equation tan θ = -√3 for θ ∈ [0, 3π] are 2π/3, 5π/3, 8π/3, and 11π/3.