Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)

tan θ = - root of 3/3

tan Ø = -√3/3

so Ø must be in quadrants II or IV
angle in standard position = 30° ( take tan^-1 (+√3/3) )

so Ø = 180-30 = 150° or Ø = 360-30 = 330°

since the period of the tangent curve is 180°

the general solution is
150° + 180k°

or in radians:
5π/6 + πk

To solve the equation tan θ = -√3/3, we need to find the values of θ that satisfy this equation.

First, we know that the tangent function is negative when it lies in the second quadrant (180 degrees < θ < 270 degrees) and the fourth quadrant (270 degrees < θ < 360 degrees). So we need to find the values of θ within these ranges.

To find the value of θ, we can take the inverse tangent (or arctan) of both sides of the equation. This will give us the angle θ.

Using a calculator or a trigonometric table, we can find the inverse tangent of -√3/3:

arctan(-√3/3) ≈ -30 degrees

However, this angle (-30 degrees) lies in the fourth quadrant. To find the corresponding angle in the second quadrant, we need to add 180 degrees to it:

θ = -30 degrees + 180 degrees = 150 degrees

So the value of θ that satisfies the equation tan θ = -√3/3 is approximately 150 degrees.

Therefore, the solution to the equation is θ = 150 degrees (or any angle that is coterminal with 150 degrees, which can be written as θ = 150 degrees + 360 degrees * k, where k is an integer).

In comma-separated list form, the answer is 150 degrees.