1. The problem states: Given $\sin 2\theta = \frac{7}{11}$, find the value of $\sin 2\theta$. 2. The formula for the sine of a double angle is $\sin 2\theta = 2 \sin \theta \cos \theta$, but here we are directly given $\sin 2\theta$. 3. Since $\sin 2\theta = \frac{7}{11}$ is already provided, the value is simply $\frac{7}{11}$. 4. Note: The user wrote $\sin 2\theta = \frac{11}{7}$, which is incorrect because sine values must be between $-1$ and $1$. The correct value is $\frac{7}{11}$ as stated first. Final answer: $$\sin 2\theta = \frac{7}{11}$$