See picture for question and answer options! you.

Ouch.
Well, let's see.

First let's get ourselves oriented.
Where in the world are we ?:
 
-- The 'csc' (cosecant) of anything is  1/sine .

-- If the csc is negative, that tells us the sine of it is also negative ... -2/5 .

-- Since the sine is negative, that means the angle is in the
3rd or 4th quadrant ... between 180° and 360°.

-- But the question also says that the angle is between π and 3π/2 .
That's the 3rd quadrant ... between 180° and 270°.

I think that helps.  That's the quadrant where the 'x's and the 'y's
are all negative.  So we can immediately throw out the middle  \
two choices.  It has to be either first or the last choice  .

The rest is kind of too hard to explain.
Please see the attached picture.