It's tan theta that is negative, not theta.
Because the tan of an angle is negative, that does not imply that the angle is negative.
Angles can be in different quadrants, giving positive or negative values of sin, cosine and tangent. The angle itself is positive.
For example, sin 90 = +1, sin 270 = -1
270 is not negative, is it? It's just in a different quadrant.