question on determining values of an angle where the tangent is a certain value

Question

How would I solve this question?

Determine the values of $\theta \in [0,2\pi]$ for which $\tan\theta = -\sqrt{\sec^2{\theta} - 1}$ is true.

Answer 1

Hint 1: It will not be true if $\tan \theta \gt 0$

Hint 2: $\sec \theta = 1/ \cos \theta$

Hint 3: $\sin^2 \theta + \cos^2 \theta =1$

Hint 4: $\tan \theta = \sin \theta / \cos \theta$