-3 = x + x + x
-3 = 3x
-3/3 = x
x = -1
The cotangent function is defined as the ratio between cosine and sine of a given angle, i.e.

Since you can't have zero at the denominator, the cotangent function is not defined when the sine is zero.
Let's look at your option:
, so the cotangent is defined here
, so the cotangent is not defined here
, so the cotangent is defined here
, so the cotangent is defined here
1/3 of all students bring lunch
2:3 is the ratio of students who bring their lunch to the number of students who do not
C. Bc it is the only one that makes sense