That's a factored equation set to zero, so either of the factors may be zero
[tex]\cot \theta + 1 = 0[/tex]
[tex]\cot \theta = -1 [/tex]
[tex]\tan \theta = \dfrac{1}{-1} = -1[/tex]
Slope of -1 in the first two quadrants is 135° aka
[tex]\theta = \dfrac{3 \pi}{4}[/tex]
Let's look at the other factor.
[tex]\sec \theta - \frac 1 2 = 0[/tex]
[tex]\sec \theta = \frac 1 2[/tex]
[tex]\cos \theta = 2 [/tex]
That has no solutions so we're left with our answer:
Answer: 3π / 4
