Solve the equation for exact solutions over the interval $[0^{\circ}, 360^{\circ}$ ).
$2 \sqrt{3} \sin 2 θ = - 3$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is ${◻}$ .
(Type an integer or a decimal. Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.)
B. The solution is the empty set.

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Final Answer: The solution set is $150, 330$ .

Steps

Step 1 ：The given equation is $2 \sqrt{3} \sin 2 θ = - 3$ .

Step 2 ：Isolate the sine function to get $\sin 2 θ = - \frac{3}{2 \sqrt{3}}$ .

Step 3 ：Simplify the right side to get $\sin 2 θ = - 0.8660254037844387$ .

Step 4 ：Use the inverse sine function to find the solutions for $2 θ$ in the interval $[0^{\circ}, 360^{\circ}]$ . The solutions are $150^{\circ}$ , $330^{\circ}$ , $120^{\circ}$ , and $300^{\circ}$ .

Step 5 ：However, we need to divide these solutions by 2 to find the solutions for $θ$ .

Step 6 ：Check if these solutions satisfy the original equation $2 \sqrt{3} \sin 2 θ = - 3$ .

Step 7 ：The solutions that satisfy the original equation are $150^{\circ}$ and $330^{\circ}$ .

Step 8 ：Final Answer: The solution set is $150, 330$ .

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