Use a calculator to give the real number value. (Be sure the calculator is in radian mode.) $\arccos (0.721)$ $\arccos (0.721) \approx$ (Round to the nearest thousandth as needed.)

Step 1 ：The problem is asking for the arccosine of 0.721. The arccosine function, also known as the inverse cosine function, returns the angle whose cosine is the given number. The output is in radians since the question specifies that the calculator should be in radian mode.

Step 2 ：Calculate the arccosine of 0.721 to get an angle of approximately 0.7655519525623249.

Step 3 ：Round the result to the nearest thousandth to get the final answer.

Step 4 ：Final Answer: \(\arccos (0.721) \approx \boxed{0.766}\)