$\begin{align}  & (2\overrightarrow{a}-\overrightarrow{b}).(\overrightarrow{b}\times \overrightarrow{c}-\overrightarrow{b}\times \overrightarrow{a}+\underbrace{\overrightarrow{c}\times \overrightarrow{c}}_{\overrightarrow{O}}-\overrightarrow{c}\times \overrightarrow{a}) \\  & =2\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})-2\underbrace{\overrightarrow{\underline{a}}.(\overrightarrow{b}\times \overrightarrow{\underline{a}}}_{tekrari})-2\underbrace{\overrightarrow{\underline{a}}.(\overrightarrow{c}\times \overrightarrow{\underline{a}}}_{tekrari})-\underbrace{\overrightarrow{\underline{b}}.(\overrightarrow{\underline{b}}}_{tekrari}\times \overrightarrow{c}) \\  & -\underbrace{\overrightarrow{\underline{b}}.(\overrightarrow{\underline{b}}}_{tekrari}\times \overrightarrow{a})+\overrightarrow{b}.(\overrightarrow{c}\times \overrightarrow{a})=2\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})+\underbrace{\overrightarrow{b}.(\overrightarrow{c}\times \overrightarrow{a})}_{\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c})}=3\overrightarrow{a}.(\overrightarrow{b}\times \overrightarrow{c}) \\ \end{align}$