Maybe a little exaggerated?

Algebra Level 4

\[\dfrac{[\sqrt{1}\sin(\theta_{1}) + \sqrt{2}\sin(\theta_{2}) + \cdots + \sqrt{100}\sin(\theta_{100})]^2}{\sin^{2}(\theta_{1}) + \sin^{2}(\theta_{2}) + \cdots + \sin^{2}(\theta_{100})}\]

Let \(\theta_{1} , \theta_{2}, \cdots,\theta_{100}\) be 100 positive real numbers.

Find the maximum value of the expression above.

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