CN-SMO 2004 Problem 5

For $\theta\in[0, \dfrac{\pi}{2}]$ , the following inequality $\sqrt{2}(2a+3)\cos(\theta-\dfrac{\pi}{4})+\dfrac{6}{\sin\theta+\cos\theta}-2\sin2\theta<3a+6$ is always true. Determine the range of $a$ .