The Solution:
The correct answer is -0.4364
Given that:

We are required to find the value of:

Step 1:
We shall find the angle represented with theta.

Recall:
The sine of angles is only negative in the 3rd and 4th quadrants.
And the formula for the 3rd quadrant is:

While the formula for the 4th quadrant is:

So,

This implies that:

Collecting the like terms, we get

We shall use the 4th quadrant formula.

Dividing both sides by -sin, we get

To check that it satisfies the given condition that says cos(theta) is greater zero, we have:

So, we have that:

Step 2:
We shall find the value of tan(theta):

Therefore, the correct answer is -0.4364