Solve the equation in degrees for all exact solutions where appropriate. Round approximate answers in degrees to the nearest tenth \[ 1-\sin 2 \theta=3 \sin 2 \theta \] Choose the correct solution set below. A. $\left\{7.2^{\circ}+180^{\circ} n, 82.8^{\circ}+180^{\circ} n\right.$, where $n$ is any integer $\}$ B. $\left\{14.5^{\circ}+180^{\circ} n, 345.5^{\circ}+180^{\circ} n\right.$, where $n$ is any integer $\}$ C. $\left\{172.8^{\circ}+180^{\circ} \mathrm{n}, 345.5^{\circ}+180^{\circ} \mathrm{n}\right.$, where $\mathrm{n}$ is any integer $\}$ D. $\left\{7.2^{\circ}+180^{\circ} \mathrm{n}, 172.8^{\circ}+180^{\circ} \mathrm{n}\right.$, where $\mathrm{n}$ is any integer $\}$ E. $\left\{14.5^{\circ}+180^{\circ} n, 165.5^{\circ}+180^{\circ} n\right.$, where $n$ is any integer $\}$

Step 1 ：Given the trigonometric equation \(1 - \sin 2 \theta = 3 \sin 2 \theta\).

Step 2 ：Rearrange the equation to isolate the trigonometric function, we get \(4 \sin 2 \theta = 1\).

Step 3 ：Divide both sides by 4, we get \(\sin 2 \theta = \frac{1}{4}\).

Step 4 ：Use the inverse sine function to find the value of \(2 \theta\), we get \(2 \theta = \sin^{-1}(\frac{1}{4})\).

Step 5 ：Solving for \(\theta\), we get \(\theta = \frac{\sin^{-1}(\frac{1}{4})}{2}\).

Step 6 ：Converting to degrees, we get two solutions \(\theta = 7.2^\circ\) and \(\theta = 82.8^\circ\).

Step 7 ：Since the sine function has a period of 180 degrees, the general solutions are \(\theta = 7.2^\circ + 180n\) and \(\theta = 82.8^\circ + 180n\), where n is any integer.

Step 8 ：\(\boxed{\text{Final Answer: The solutions to the equation are } \{7.2^\circ + 180^\circ n, 82.8^\circ + 180^\circ n\}, \text{ where n is any integer.}}\)