\(
Let\\ f(\theta )=\frac { 1 }{ { tan }^{ 9 }\theta } \left( { \left( 1+{ tan\theta } \right) }^{ 10 }+{ \left( 2+{ tan\theta } \right) }^{ 10 }+\quad ...\quad +{ \left( 20+{ tan\theta } \right) }^{ 10 } \right) \quad \\-20tan\theta \\The\quad left\quad hand\quad limit\quad of\quad f(\theta )\quad as\quad \theta \rightarrow \frac { \pi }{ 2 } \quad is
\)

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