If $\overrightarrow a = 2\widehat i + \widehat j + 2\widehat k$, then the value of

${\left| {\widehat i \times \left( {\overrightarrow a \times \widehat i} \right)} \right|^2} + {\left| {\widehat j \times \left( {\overrightarrow a \times \widehat j} \right)} \right|^2} + {\left| {\widehat k \times \left( {\overrightarrow a \times \widehat k} \right)} \right|^2}$ is equal to____