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public class UnityConsoleTraceListener : TextWriterTraceListener
{
    public override void Write(string message)
    {
      UnityEngine.Debug.LogError(message);
      base.Write(message);
    }

    public override void WriteLine(string message)
    {
      UnityEngine.Debug.LogError(message);
      base.WriteLine(message);
    }
}

somewhere in Unity Code at the earliest point possible: 

System.Diagnostics.Debug.Listeners.Add(new UnityConsoleTraceListener());