Let S={θ ∈[0,2 π]-{(π)/2, (3 π)/2}: sin^-1( sin θ)+ cos^-1( cos θ)+ tan^-1( tan θ)=(4 π)/5}. Then 30/(π) Σ_θ ∈ S θ is equal to \ \ \ \.

Let $\displaystyle S=\left\{\theta \in[0,2 \pi]-\left\{\frac{\pi}{2}, \frac{3 \pi}{2}\right\}: \sin ^{-1}(\sin \theta)+\cos ^{-1}(\cos \theta)+\tan ^{-1}(\tan \theta)=\frac{4 \pi}{5}\right\}$. Then $\displaystyle \frac{30}{\pi} \sum_{\theta \in S} \theta$ is equal to \_\_\_\_.