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Consider a \( \triangle A B C \). A directly similar \( \triangle A_{1} B_{1} C_{1} \) is inscribed
P in the \( \triangle A B C \) such that \( A_{1}, B_{1} \) and \( C_{1} \) are the interior points of the sides \( A C, A B \) and \( B C \), respectively. Prove
W
\[
\text { that } \frac{\operatorname{Area}\left(\Delta A_{1} B_{1} C_{1}\right)}{\operatorname{Area}(\triangle A B C)} \geq \frac{1}{\operatorname{cosec}^{2} A+\operatorname{cosec}^{2} B+\operatorname{cosec}^{2} C}
\]
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