Use the addition formula and \(\tan135^\circ=-1\). Writing \(T=\tan\theta\), \[k=\frac{T-1}{1+T}.\] Thus \[k+kT=T-1\quad\Rightarrow\quad(k-1)T=-1-k,\] \[\boxed{\tan\theta=\frac{1+k}{1-k}}.\] This expression applies where \(\tan\theta\) is defined; \(k=1\) corresponds to an undefined \(\tan\theta\).