If a =2 i + j +2 k, then the value of | i ×( a × i )|^2+| j ×( a × j )|^2+ | k ×( a × k )|^2 is equal to \ \ \ \.

If $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}+\hat{j}+2 \hat{k}$, then the value of $$|\hat{i} \times(\overrightarrow{\mathrm{a}} \times \hat{i})|^2+|\hat{j} \times(\overrightarrow{\mathrm{a}} \times \hat{j})|^2+ $$ $\displaystyle |\hat{\boldsymbol{k}} \times(\overrightarrow{\mathbf{a}} \times \hat{\boldsymbol{k}})|^2$ is equal to \_\_\_\_.