Unconditional expectation of the error term

Problem

In a LRM with exogeneity we have the conditional expectations

\[E\left( ε_i \mid x_i \right)=0\]

Show that the unconditional expectation is zero as well,

\[E\left( ε_i \right)=0\]

To do this, we us “Law of iterated expectations”. For arbitrary random variables \(X,Y\) is states that

\[E\left( Y \right)=E\left( E\left( Y \mid X \right) \right)\]