Find cottheta if cactus theta = -square root 37/6

The question is not clear but I will solve it for all the possible conditions.

If cosФ = - √37 ÷ 6

Which means,
Adjacent = - √37
Hypotenuse = 6

This is not possible because hypotenuse cannot be smaller.

If cosecФ = - √37 ÷ 6

Which means,
Opposite = 6 
Hypotenuse = - √37

Using Pythagoras theorem,

Adjacent = (Hypotenuse)² - (Opposite)²

Adjacent = √{(- √37)² - (6)²}

Adjacent = √{(37 - 36}

Adjacent = √{(1}

Adjacent = 1

Now we have all the three sides of a right triangle, therefore, we can find out the value for cotФ.
That is;

cotФ = adjacent ÷ opposite

cotФ =