A 35-year-old man with known rheumatic heart disease on warfarin presents with acute dyspnea and hemoptysis. On examination, he has signs of acute pulmonary edema and a new pulsatile hepatomegaly. Chest X-ray shows pulmonary edema with a normal cardiac silhouette. Transthoracic echocardiography shows severe tricuspid regurgitation with right ventricular dilatation and a mobile echo density in the right atrium. Which investigation is most appropriate to confirm the diagnosis and guide immediate management?