If \( A, B \), and \( C \) are the angles of non-right angled triangle \( A B C \), then find th...

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If \( A, B \), and \( C \) are the angles of non-right angled triangle \( A B C \), then find the value of
\[
\left|\begin{array}{ccc}
\tan A & 1 & 1 \\
1 & \tan B & 1 \\
1 & 1 & \tan C
\end{array}\right|
\]
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