A Few Good Trig Identities

Geometry Level 2

\[ \dfrac { 1 }{ 1+\sin^{2} {x} } +\dfrac { 1 }{ 1+\cos^{2} {x} } +\dfrac { 1 }{ 2+\tan ^{2} {x} } +\dfrac { 1 }{ 2+\cot ^{ 2 }{ x } } \]

For all \(x\) on the domain of the \(\tan x\) and \(\cot x,\) what is the value of the expression above?

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