1. **State the problem:** Find the value of $\arccos\left(\frac{4}{3 \times \sqrt{2}}\right)$. 2. **Recall the domain of arccos:** The function $\arccos(x)$ is defined only for $x$ in the interval $[-1,1]$. 3. **Calculate the argument:** Compute the value inside the arccos: $$\frac{4}{3 \times \sqrt{2}} = \frac{4}{3\sqrt{2}}.$$ 4. **Approximate the denominator:** $3 \times \sqrt{2} \approx 3 \times 1.414 = 4.242$. 5. **Evaluate the fraction:** $\frac{4}{4.242} \approx 0.943$. 6. **Check domain:** Since $0.943$ is within $[-1,1]$, $\arccos(0.943)$ is defined. 7. **Find the angle:** Use a calculator or table to find $\arccos(0.943)$. This is approximately $0.339$ radians. **Final answer:** $$\arccos\left(\frac{4}{3 \sqrt{2}}\right) \approx 0.339 \text{ radians}.$$