Answer
Negative.
Work Step by Step
$90^{\circ}\lt\theta\lt 180^{\circ}\implies180^{\circ}\lt2\theta\lt 360^{\circ}$
Cosecant function is negative as the angle $2\theta$ is in between $180^{\circ}$ and $360^{\circ}$( third and fourth quadrants).
Precalculus (6th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
013421742X
ISBN 13:
978-0-13421-742-0
Chapter 5 - Trigonometric Functions - 5.2 Trigonometric Functions - 5.2 Exercises - Page 520: 154
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