If \( \int_{\sin x}^{1} t^{2} f(t) d t=1-\sin x \), where \( x \in\left(0, \frac{\pi}{2}\right) ...

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If \( \int_{\sin x}^{1} t^{2} f(t) d t=1-\sin x \), where \( x \in\left(0, \frac{\pi}{2}\right) \), then find the value of \( f\left(\frac{1}{\sqrt{3}}\right) \).
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