Question

Find the smallest positive angle θ in the third quadrant for which tan(θ) = 1. ...?

Answer 1

Here is the explanation as to how to find the smallest positive angle θ in the third quadrant for which tan(θ) = 1. 
The only instance that you can have a tangent theta equal to one, both values of sine and cosine must be the same. This happens at every 45 degree angle in each quadrant. So for the third quadrant, it would be 225. To get the 225, the angle in the first quadrant is 45 degrees. You add 90 degrees every quadrant. 
Hope this answer helps.