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.