If \(5\sin\theta=4\), then the value of \(\frac{\cosec\theta-\cot\theta}{\cosec\theta+\cot\theta}\) is
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When \(\sin\theta=\frac{4}{5}\), use the \(3-4-5\) triangle. Then \(\cos\theta=\frac{3}{5}\), \(\cosec\theta=\frac{5}{4}\), and \(\cot\theta=\frac{3}{4}\).