Let $\theta$ be the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, where $\left|\overrightarrow{a}\right|=4,\left|\overrightarrow{b}\right|=3 \theta \in \left(\frac{\pi }{4},\frac{\pi }{3}\right)$. Then $\left|\right(\overrightarrow{a}-\overrightarrow{b})\times (\overrightarrow{a}+\overrightarrow{b}){|}^2+4(\overrightarrow{a}·\overrightarrow{b}{)}^2$ is equal to

$$\begin{gathered} \left|\overrightarrow{a}\right|=4,\left|\overrightarrow{b}\right|=3 \theta \in \left(\frac{\pi }{4},\frac{\pi }{3}\right) \\ \left|\right(\overrightarrow{a}-\overrightarrow{b})\times (\overrightarrow{a}+\overrightarrow{b}){|}^2+4(\overrightarrow{a}·\overrightarrow{b}{)}^2 \end{gathered}$$

$$\begin{gathered} |\overrightarrow{a}\times \overrightarrow{b}-\overrightarrow{b}\times \overrightarrow{a}{|}^2+4a^2{b}^2{\cos }^2\theta \\ 4|\overrightarrow{a}\times \overrightarrow{b}{|}^2+4a^2{b}^2{\cos }^2\theta \\ 4a^2{b}^2{\sin }^2\theta +4a^2{b}^2{\cos }^2\theta \\ 4a^2{b}^2=4\times 16\times 9=576 \end{gathered}$$