Let f(θ)=3( sin^4((3 π)/2-θ)+ sin^4(3 π+θ))-2(1- sin^2 2 θ) and S={θ ∈[0, π]: f^′(θ)=-(√ 3)/2}. If 4 β=Σ_θ ∈ S θ, then f(β) is equal to

Let $\displaystyle f(\theta)=3\left(\sin ^4\left(\frac{3 \pi}{2}-\theta\right)+\sin ^4(3 \pi+\theta)\right)-2\left(1-\sin ^2 2 \theta\right)$ and $\displaystyle S=\left\{\theta \in[0, \pi]: f^{\prime}(\theta)=-\frac{\sqrt{3}}{2}\right\}$. If $\displaystyle 4 \beta=\sum_{\theta \in S} \theta$, then $\displaystyle f(\beta)$ is equal to