$\frac{{\sin }^3 \mathrm{\theta }-{\cos }^3 \mathrm{\theta }}{\sin \mathrm{\theta }-\cos \mathrm{\theta }}-\frac{\cos \mathrm{\theta }}{\sqrt{1+{\cot }^2 \mathrm{\theta }}}-2\tan \mathrm{\theta } \cot \mathrm{\theta }=-1,$ if

$$\begin{gathered} \frac{{\sin }^3 \mathrm{\theta }-{\cos }^3 \mathrm{\theta }}{\sin \mathrm{\theta }-\cos \mathrm{\theta }}-\frac{\cos \mathrm{\theta }}{\sqrt{1+{\cot }^2 \mathrm{\theta }}}-2\tan \mathrm{\theta } \cot \mathrm{\theta } \\ \frac{\left(\mathrm{sin\theta }-\mathrm{cos\theta }\right)\left(1+\mathrm{sin\theta } \mathrm{cos\theta }\right)}{\mathrm{sin\theta }-\mathrm{cos\theta }}-\left|\mathrm{sin\theta }\right|\mathrm{cos\theta }-2=-1 \\ 1+\mathrm{sin\theta } \mathrm{cos\theta }-\left|\mathrm{sin\theta }\right|\mathrm{cos\theta }=1 \\ \mathrm{sin\theta }>0 \\ \mathrm{\theta }\in \left(\frac{\mathrm{\pi }}{2},\mathrm{\pi }\right) \end{gathered}$$