We have,
$$
\begin{aligned}
& \operatorname{cosec} \theta-\cot \theta=2017 \\
& \therefore \operatorname{cosec} \theta+\cot \theta=\frac{1}{2017} \\
& {\left[\begin{array}{l}
\because \operatorname{cosec}^2 \theta-\cot ^2 \theta=1 \\
\Rightarrow \operatorname{cosec} \theta-\cot \theta=\frac{1}{\operatorname{cosec} \theta+\cot \theta}
\end{array}\right]}
\end{aligned}
$$
Adding Eqs. (i) and (ii), we get
$$
\begin{aligned}
2 \operatorname{cosec} \theta & =2017+\frac{1}{2017} \\
\Rightarrow \operatorname{cosec} \theta & =\frac{1}{2}\left[2017+\frac{1}{2017}\right]>0
\end{aligned}
$$
$\theta$ lie in Ist or Ind quadrant.
Subtracting Eq. (i) from Eq. (ii), we get
$$
2 \cot \theta=\frac{1}{2017}-2017
$$


$$
\cot \theta=\frac{1}{2}\left(\frac{1}{2017}-2017\right) < 0
$$
$\therefore \theta$ lie in Ind and IIIrd quadrant.
Hence, $\theta$ lies in Ind quadrant.