Vector Algebra

If \(\theta\) is angle between the vectors \(\bar{a}\) and \(\bar{b}\) where \(|\bar{a}|=4,|\bar{b}|=3\) and \(\theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)\), then \(|(\bar{a}-\bar{b}) \times(\bar{a}+\bar{b})|^2+4(\bar{a} \cdot \bar{b})^2\) has the value