Answer
$$A=(4\sqrt 3-\frac{4}{3}\pi)$$
Work Step by Step
$$A=4\times \int_{0}^{\pi/6}\frac{1}{2}(8cos(2\theta)-4)d \theta=2[4sin(2\theta)-4\theta]_{0}^{\pi/6}$$
Hence, $$A=(4\sqrt 3-\frac{4}{3}\pi)$$
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