The standard or usual treatment for patients diagnosed with deep vein thrombosis or pulmonary embolism is treatment with blood thinners (called anticoagulants). While treatment of blood clots with blood thinners is effective, some research has shown that adding a statin (medication used to lower cholesterol) may give extra protection. It is thought that statins can improve how cells along the walls of the vein control inflammation, which can prevent new blood clots from forming. The medication in this study, rosuvastatin, is approved in Canada for use as a cholesterol-lowering medication. The use of rosuvastatin in this study is considered investigational. This means that Health Canada has not approved the use of rosuvastatin as a treatment for blood clots. However, it has been approved for use in this research study. The purpose of this study is to examine if adding a statin (rosuvastatin) to the usual blood thinner treatment will decrease the risk of another blood clot forming. The investigators also hope to discover if taking a statin reduces damage to your veins. To do this, some of the participants in this study will get rosuvastatin and others will receive a placebo (a substance that looks like the study rosuvastatin but does not have any active or medicinal ingredients). The placebo in this study is not intended to have any effect on your blood clot. A placebo is used to make the results of the study more reliable.