Mathematics Question from JEE Main 2023 · 24 January, Shift 2

Let $S = \{ \theta \in [0, 2\pi) : \tan(\pi \cos \theta) + \tan(\pi \sin \theta) = 0 \}$. Then $\sum_{\theta \in S} \sin^2 \left(\theta + \frac{\pi}{4}\right)$ is equal to:](streamdown:incomplete-link)