$2 \cos (3 \theta)=-\sqrt{2}$

Step 1 ：Divide both sides of the equation by 2 to isolate \(\cos (3 \theta)\): \(\cos (3 \theta) = -\frac{\sqrt{2}}{2}\)

Step 2 ：Use the inverse cosine function to find the value of \(3 \theta\): \(3 \theta = \cos^{-1}(-\frac{\sqrt{2}}{2})\)

Step 3 ：Calculate the value of \(3 \theta\): \(3 \theta = 2.356194490192345\)

Step 4 ：Divide by 3 to find the value of \(\theta\): \(\theta = \frac{2.356194490192345}{3}\)

Step 5 ：Calculate the value of \(\theta\): \(\theta = 0.7853981633974483\)

Step 6 ：Convert \(\theta\) to degrees: \(\theta = 45.0\) degrees

Step 7 ：Final Answer: The solution to the equation \(2 \cos (3 \theta)=-\sqrt{2}\) is \(\boxed{45}\) degrees