Final answer:
The value of theta is approximately 303.69 degrees.
Step-by-step explanation:
The given problem is asking us to find the value of theta (theta) when tan(theta) = -3/2 and 270 < theta < 360. To solve this, we need to find the angle whose tangent is -3/2. Since the tangent function is negative in the third and fourth quadrants, we can use the inverse tangent function to find the angle. Using a calculator, we find that tan^-1(-3/2) is approximately -56.31 degrees. However, since the angle is given to be between 270 and 360 degrees, we need to find the equivalent positive angle. Adding 360 degrees to -56.31 degrees, we get 303.69 degrees. Therefore, theta is approximately 303.69 degrees.