Let \( f(\theta) = 3\Big(\sin^4\!\left(\dfrac{3\pi}{2}-\theta\right) + \sin^4(3\pi+\theta)\Big) - 2(1-\sin^2 2\theta) \) 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:
