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To solve for the value of \(\(\cos^{-1}(0.7190)\)\), we need to find the angle in radians whose cosine is 0.7190.

1. Identify the given value: We are given that the cosine of an angle is 0.7190.

2. Use the inverse cosine function: To find the angle itself, we would use the inverse cosine function, denoted as \(\(\cos^{-1}\)\). This function will give us the angle whose cosine is 0.7190.

3. Compute the angle: When we compute \(\(\cos^{-1}(0.7190)\)\), we obtain an angle value.

4. Round the result: This computed angle should be rounded to three decimal places.

Following these steps, we find that:
\(\[ \cos^{-1}(0.7190) \approx 0.768 \text{ radians} \]\)

So, the approximate value of \(\(\cos^{-1}(0.7190)\)\), rounded to three decimal places, is \(\(0.768\)\) radians.

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