$ \Rightarrow  \tan\theta \propto T_1$

$ \Rightarrow  \tan\theta = kT_1 $… $(i)$

and $ R_2 \propto T_2$

$\Rightarrow  \tan (90^o -\theta) \propto T_2$ 

$ \Rightarrow  \cot\theta = kT_2$ ….$(ii)$

From equation $(i)$ and $(ii)$ $k({T_2} - {T_1}) = (\cot \theta - \tan \theta )\,$

$\,({T_2} - {T_1}) = \left( {\frac{{\cos \theta }}{{\sin \theta }} - \frac{{\sin \theta }}{{\cos \theta }}} \right) = \frac{{({{\cos }^2}\theta - {{\sin }^2}\theta )}}{{\sin \theta \cos \theta }}$$ = 2\cot 2\theta $

$ \Rightarrow $ $(T_2 -T_1) \propto \cot 2\theta$