To find the value of \(\tan(\pi - \theta)\), we can use the tangent subtraction identity.
The tangent function has the property:
\[ \tan(\pi - \theta) = -\tan(\theta) \]
Thus, the correct completion for the identity is:
\[ \tan(\pi - \theta) = -\tan(\theta) \]
So, the answer is:
\(- \tan(\theta)\)