Cube root of Unity.

Algebra Level 3

\( If\quad { z }^{ 2 }+z+1\quad =\quad 0\quad Where\quad z\quad is\quad a\quad complex\quad number,\\ then\quad find\quad value\quad of\quad \\ { ({ z }^{ 1 }+\frac { 1 }{ { z }^{ 1 } } ) }^{ 2 }+{ ({ z }^{ 2 }+\frac { 1 }{ { z }^{ 2 } } ) }^{ 2 }+{ ({ z }^{ 3 }+\frac { 1 }{ { z }^{ 3 } } ) }^{ 2 }+...+{ ({ z }^{ 6 }+\frac { 1 }{ { z }^{ 6 } } ) }^{ 2 }\quad \)

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