Oh my log!

Algebra Level 4

Given that \( { a }^{ 2 }={ b }^{ 3 }={ c }^{ 5 }={ d }^{ 6 } \),

let \( \log _{ d }{ abc } = \frac { m }{ n } \) where m and n are co-prime integers

then \( \frac { { tan }^{ -1 }(m) }{ n } =\quad ?\)

give your answer to 2 decimal places. Calculate in radians.

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