Let S={θ ∈[0,2 π): tan (π cos θ)+ tan (π sin θ)=0}. Then Σ_θ ∈ S sin^2(θ+(π)/4) is equal to ____.

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