determine two angles between $0^{\circ}$ and $360^{\circ}$ that have a secant of $-\sqrt{2}$. Include a diagram in your solution.

Step 1 ：The secant of an angle is defined as the reciprocal of the cosine of the angle. So, we need to find the angles whose cosine is \(-\frac{1}{\sqrt{2}}\).

Step 2 ：The cosine function is negative in the second and third quadrants. So, we need to find the reference angle in the first quadrant whose cosine is \(\frac{1}{\sqrt{2}}\) and then find the corresponding angles in the second and third quadrants.

Step 3 ：The reference angle whose cosine is \(\frac{1}{\sqrt{2}}\) is \(45^\circ\).

Step 4 ：So, the angles in the second and third quadrants are \(180^\circ-45^\circ=135^\circ\) and \(180^\circ+45^\circ=225^\circ\) respectively.

Step 5 ：Final Answer: The two angles between \(0^\circ\) and \(360^\circ\) that have a secant of \(-\sqrt{2}\) are \(\boxed{135^\circ}\) and \(\boxed{225^\circ}\).