Step 1 :Given that \(\tan t = \frac{4}{9}\)
Step 2 :We know that \(\tan (t-\pi) = \tan t\)
Step 3 :Substitute the given value: \(\tan (t-\pi) = \frac{4}{9}\)
Step 4 :\(\boxed{\tan (t-\pi) = \frac{4}{9}}\)