Step 1 :Find two values of \(0,0 \leq 0<2 \pi\), that satisfy the following equation. \[\cos \theta=-\frac{\sqrt{2}}{2}\]
Step 2 :The cosine function has a value of \(-\frac{\sqrt{2}}{2}\) at two points in the interval \([0, 2\pi)\), namely at \(\frac{3\pi}{4}\) and \(\frac{5\pi}{4}\). These are the two solutions to the equation.
Step 3 :Final Answer: The two values of \(\theta\) that satisfy the equation \(\cos \theta=-\frac{\sqrt{2}}{2}\) are \(\boxed{\frac{3\pi}{4}}\) and \(\boxed{\frac{5\pi}{4}}\).