Problem source

The diagram shows a crude step-ladder constructed by smoothly hinging-together
two light ladders $AB$ and $AC,$ each of length $l,$ at $A$. A
uniform rod of wood, of mass $m$, is pin-jointed to $X$ on $AB$
and to $Y$ on $AC$, where $AX=\frac{3}{4}l=AY.$ The angle $\angle XAY$
is $2\theta.$ 

\noindent \begin{center}
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\par\end{center}

The rod $XY$ will break if the tension in it exceeds $T$. The step-ladder
stands on rough horizontal ground (coefficient of friction $\mu$).
Given that $\tan\theta>\mu,$ find how large a mass $M$ can safely
be placed at $A$ and show that if 
\[
\tan\theta>\frac{6T}{mg}+4\mu
\]
the step-ladder will fail under its own weight. 

{[}You may assume that friction is limiting at the moment of collapse.{]}