Answer
It is unnecessary because we do not have to use Identities which involve second-power trigonometric functions.
Work Step by Step
The quadrant of $\theta$ is given to signify the signs of $\sin\theta$. In detail, if $\theta$ lies in quadrant I and II, $\sin\theta$ is positive. If $\theta$ lies in quadrant III and IV, $\sin\theta$ is negative.
This fact must be given in the situation when to find $\sin\theta$, we end up with 2 results of $\sin\theta$ that are opposite in signs. These happen a lot in trigonometric identities, since a lot of identities involve dealing with the second power, which would lead to 2 opposite-signed results when we decrease to the first power.
For example, look at this Pythagorean Identity, $$\sin^2\theta+\cos^2\theta=1$$
$$\sin^2\theta=1-\cos^2\theta$$
$$\sin\theta=\pm(1-\cos^2\theta)$$
As you can see, when we decrease to the first power, we end up with an opposite sign like that. Therefore, the quadrant of $\theta$ is essential to decide which result to choose.
On the other hand, in exercises 17 and 18, we only need to use this identity:
$$\csc\theta=\frac{1}{\sin\theta}$$
$$\sin\theta=\frac{1}{\csc\theta}$$
Here we would end up with only 1 result of $\sin\theta$. So there is no need for quadrant of $\theta$.
