Answer:
tan theta = -4/3.
Explanation:
The inequality means that theta is in the 4th quadrant ( between 270 and 360 degrees.
The angle whose sine is 4/5 is 53.13 degrees.
So the angle whose sine is -4/5 is 306.87 degrees.
The tangent is negative and the triangle formed by the angle in the 4th quadrant has sides 3, - 4 and 5 ( by the Pythagoras theorem).
So tan theta = opposite / adjacent = -4/3 (answer).