Answer :

The change in angle ABC is calculated using trigonometry.
$ \cos \theta =\frac{l_{1}^{2}+l_{3}^{2}-l_{2}^{2}}{2{{l}_{3}}{{l}_{1}}} $

The change in angle ABC is given as when the above equation is differentiated.

$ d\theta =\frac{2\left( {{\alpha }_{2}}-{{\alpha }_{1}} \right)\Delta T}{\sqrt{3}} $