Solve the equation for solutions over the interval $[0^{\circ },{360}^{\circ })$.
$${\csc }^2\theta -2\cot \theta =0$$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is $\{◻$.
(Type your answer in degrees. Do not include the degree symbol in your answer. Round to one decimal place as needed. Use a comma to separate answers as needed.)
B. The solution is the empty set.

Step 1 ：Given the equation ${\csc }^2\theta -2\cot \theta =0$, we need to solve for $\theta$ over the interval $[0^{\circ },{360}^{\circ })$.

Step 2 ：We can rewrite the equation in terms of sine and cosine for easier manipulation. The cosecant is the reciprocal of the sine function and the cotangent is the reciprocal of the tangent function, which is cosine over sine. So, the equation becomes: $$\frac{1}{{\sin }^2\theta }-2\frac{\cos \theta }{\sin \theta }=0$$

Step 3 ：We can multiply through by ${\sin }^2\theta$ to clear the fractions: $$1-2\cos \theta \sin \theta =0$$

Step 4 ：This can be rearranged to: $$2\cos \theta \sin \theta =1$$

Step 5 ：This is a form of the double angle identity for sine, $2\sin \theta \cos \theta =\sin 2\theta$. So, we can rewrite the equation as: $$\sin 2\theta =1$$

Step 6 ：We can solve this equation for $\theta$ over the interval $[0^{\circ },{360}^{\circ })$. The solutions to the equation are the values of $\theta$ for which $\sin 2\theta =1$. The solutions are approximately 45 degrees and 225 degrees. These are the angles for which the sine function equals 1 in the interval $[0^{\circ },{360}^{\circ })$.

Step 7 ：Final Answer: The solution set is $\boxed{{\displaystyle 45,225}}$.