Find an angle between $0^{\circ}$ and $360^{\circ}$ that is coterminal with $810^{\circ}$

Step 1 ：To find an angle that is coterminal with \(810^{\circ}\), we need to subtract or add multiples of \(360^{\circ}\) until we get an angle between \(0^{\circ}\) and \(360^{\circ}\).

Step 2 ：Subtract \(360^{\circ}\) from \(810^{\circ}\) twice to get \(90^{\circ}\).

Step 3 ：Final Answer: The angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with \(810^{\circ}\) is \(\boxed{90^{\circ}}\).