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If \(\displaystyle \lim_{x \to 0} \int_0^x \frac {t^2 \ dt}{(x-\sin x)\sqrt{a+t}} = 1\), what is the value of \(a\)?

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\[\large \int_{0}^{\pi} \dfrac{\text{d}\theta}{6+4\cos\theta} = \ ?\]

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