 This is a Phase IIa, open-label, single-arm, multi-center study to evaluate the efficacy and safety of orally administered MEK inhibitor trametinib as the second line in subjects with advanced or metastatic biliary tract cancers BTC in Japanese population. The primary endpoint of this study is 12 week non-progressive disease PD rate defined as the percentage of subjects without progression at Week 12. As a sub-study, pharmacokinetics PK of four tablets of 0.5 milligram mg tablet, or one tablet of 2 mg tablet to achieve 2 mg daily regimen will be assessed to evaluate the pharmacokinetics of trametinib in Japanese population. 