$\cot 16°\cot 44°+\cot 44°\cot 76°-\cot 76°\cot 16°=$

$$\begin{gathered} \cot \left(A+B\right)=\frac{\cot \mathrm{A}\cdot \cot \mathrm{B}-1}{\cot \mathrm{A}+\cot \mathrm{B}} \\ \Rightarrow \begin{array}{l}\cot (60°)=\cot (16°+44°)\\ \frac{1}{\sqrt{3}}=\frac{\cot 16°\cot 44°-1}{\cot 16°+\cot 44°}\\ \cot 16°\cot 44°=\frac{\cot 16°+\cot 44°}{\sqrt{3}}-1\dots \dots .\left(1\right)\\ \begin{array}{l}simillarly\cot 44°\cot 76°=\frac{\cot 44°+\cot 76°}{-\sqrt{3}}+1\dots \dots \left(2\right)\\ \\ \cot 76°\cot 16°=\frac{\cot 16°-\cot 76°}{\sqrt{3}}-1\dots \dots \dots \left(3\right)\\ \begin{array}{l}\cot 16\cot 44°+\cot 44°\cot 76°-\cot 76°\cot 16°\\ =\frac{{\displaystyle \cot 16°+\cot 44}}{{\displaystyle \sqrt{3}}}+1-\left[\frac{\cot 44°+\cot 76°}{\sqrt{3}}\right]+1-\left[\frac{\cot 16°-\cot 76°}{\sqrt{3}}\right]+1\\ =3\end{array}\end{array}\end{array} \end{gathered}$$