Trigonometri #1

Geometry Level 1

\[ \large\frac { 1 }{ \cos ^{ 2 }{ \theta } } +\frac { 1 }{ 1+\sin ^{ 2 }{ \theta } } +\frac { 2 }{ 1+\sin ^{ 4 }{ \theta } } +\frac { 4 }{ 1+\sin ^{ 8 }{ \theta } } \]

If \( \large \sin ^{ 16 }{ \theta } = \frac { 1 }{ 5 } \), what is the value of the expression above?