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