Suppose \(f(x) = \displaystyle\int_{\pi/3}^{x} \dfrac{\sin(t)}{t} \, dt \).

Now let \(\displaystyle\alpha = \dfrac{\pi}{2} f(\pi/2)- \int_{\pi/3}^{\pi/2} f(x)\, dx \).

Then find the value of \(356 \times \alpha \).

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