First, calculate the length of OC using the cosine of angle AOB:

\(OC = 6 \cos 0.8 = 4.18 \text{ cm}\).

Next, find the area of sector OCD:

\(\text{Area of sector } OCD = \frac{1}{2} \times (4.18)^2 \times 0.8\).

Then, calculate the area of triangle OCA:

\(\Delta OCA = \frac{1}{2} \times 6 \times 4.18 \times \sin 0.8\).

Finally, find the required area of the shaded region by subtracting the area of sector OCD from the area of triangle OCA:

\(\text{Required area} = \Delta OCA - \text{sector } OCD\).

The calculated area is approximately 2.01 cm².