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

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

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