How do I get a given profile's default RecordType for Opportunity?

The closest I can get is the default record type for the current user:

//find all Opportunity record types
List<Schema.RecordTypeInfo> infos = Schema.SObjectType.Opportunity.RecordTypeInfos;
Id defaultRecordTypeId;

//check each one
for (Schema.RecordTypeInfo info : infos) {
  if (info.DefaultRecordTypeMapping) {
    defaultRecordTypeId = info.RecordTypeId;
  }
}

//here is the default Opportunity RecordType Id for the current user
System.debug(defaultRecordTypeId);

Got it....

if (ApexPages.currentPage().getParameters().get('RecordType') == null) {
    Schema.DescribeSObjectResult describeOpp = Schema.SObjectType.Opportunity;    
    List<Schema.RecordTypeInfo> rtInfos = describeOpp.getRecordTypeInfos();
    for(Schema.RecordTypeInfo rtInfo : rtInfos) {
        if(rtInfo.isDefaultRecordTypeMapping()) {               
            ApexPages.currentPage().getParameters().put('RecordType', rtInfo.getRecordTypeId());
            break;
        }
    }
    }
      String recordRT = ApexPages.currentPage().getParameters().get('RecordType');