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. $\{{7.2}^{\circ }+{180}^{\circ }n,{82.8}^{\circ }+{180}^{\circ }n$, where $n$ is any integer $\}$
B. $\{{14.5}^{\circ }+{180}^{\circ }n,{345.5}^{\circ }+{180}^{\circ }n$, where $n$ is any integer $\}$
C. $\{{172.8}^{\circ }+{180}^{\circ }\mathrm{n},{345.5}^{\circ }+{180}^{\circ }\mathrm{n}$, where $\mathrm{n}$ is any integer $\}$
D. $\{{7.2}^{\circ }+{180}^{\circ }\mathrm{n},{172.8}^{\circ }+{180}^{\circ }\mathrm{n}$, where $\mathrm{n}$ is any integer $\}$
E. $\{{14.5}^{\circ }+{180}^{\circ }n,{165.5}^{\circ }+{180}^{\circ }n$, 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 ：$\boxed{{\displaystyle \text{Final Answer: The solutions to the equation are }\{{7.2}^{\circ }+{180}^{\circ }n,{82.8}^{\circ }+{180}^{\circ }n\},\text{ where n is any integer.}}}$