Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation.
Given $r =\sqrt 3 - 2 \sin θ$
Table of Values:
$(\sqrt 3, 0)$
$(\sqrt 3- 1, \frac{\pi}{6})$
$(\sqrt 3 - 2, \frac{\pi}{2})$
$(\sqrt 3 - 1, \frac{5\pi}{6})$
$(\sqrt 3, \pi)$
$(\sqrt 3 + 1, \frac{7\pi}{6})$
$(\sqrt 3 + 2, \frac{3\pi}{2})$
$(\sqrt 3 + 1, \frac{11\pi}{6})$
See graph below. It is in the shape of a cardoid (with a loop).