SOLUTION: if 0 is less or equal to theta and theta is less or equal to 380 degrees, then determine all values of theta (to the nearest degree)that satisfy tan theta = -2.1445

First we find the reference angle for θ, which is between 0° and 90°
by finding the inverse tangent of |-2.1445| or 2.1445 
That is 64.99992918° which to the nearest degree is 65°

the tangent is negative in the 2nd and 4th quadrants.

We get the angles between 0° and 360° which θ could be.

To get the angle in the 2nd quadrant, we subtract 65° from 180° and get θ=115°.
To get the angle in the 4th quadrant, we subtract 65° from 360° and get θ=295°.

Those are both solutions.

Note: We would be able to add or subtract 360° to either of those as many times
as we like as long as we didn't go out of the domain ,
but adding or subtracting 360° even once goes out of that domain, so those two
are the only answers:

Answers: θ=115° and θ=295°  are the only answers.

Edwin