I am sorry to learn about your difficult situation. Unfortunately, the scenario you are facing is very common, especially in America. I am not familiar with the Canadian mental health system. Generally, in the American mental health system, an individual must be homicidal or suicidal to be admitted into a hospital involuntarily. Not all states have such strict standards but the essence of most laws in the United States is that an individual has to be very ill before they can be hospitalized against their will.
It is unlikely that you will be successful in “persuading” your brother to undergo treatment. In most cases, it will be a frustrating and unwinnable battle. You can and should try everything you can think of but understand that it will likely be difficult. If he is actively psychotic, then he is unable to think clearly. It is difficult to successfully utilize logic and reason with an individual who can’t process logical or reasonable thoughts.
Your brother has extreme periods of rage and has mentioned killing people. He is unwilling to seek treatment on his own and he is out of control. This makes him a potential danger to your family and to others. In this case, you should not hesitate to call the authorities.
My advice is to continue to call the authorities as many times as necessary. At this time, your brother may be a danger to other people. Be certain that the authorities are aware of this fact.
I would also encourage you to search for Canadian mental health system Internet resources. In America, there are advocacy organizations such as the National Alliance For Mental Illness (NAMI) and the Treatment Advocacy Center, both designed to help family members who have a loved one with a mental illness, navigate the mental health system. Here’s a link to the NAMI Ontario website.
I wish you the best of luck. Please take care.