When was he sentenced? When did this evidence get discovered? Did the previous attorney know about the video but do nothing?
I suggest that you consult with an attorney immediately to try and determine what the options are - one who has done Writs and Appeals.
Sorry but there is nothing that you can do. Your brother pled which means there is generally no appeal. Before he entered his plea, he would have been questioned extensively by the judge, including being asked if he understood the charges, if he had enough time to talk to his attorney and if he had any questions of his attorney or judge. He would have been asked if he made his plea knowingly, intelligently and voluntarily and whether he was threatened or coerced. A video that explains why he did the carjacking still means the did the carjacking, so that's no help . Given that he got 21 years, I suspect he used a gun which adds 10 years and possible had a one year prison prior. Even if he could appeal, he would need a certificate of appealability from the sentencing judge which means that there would be an issue to appeal. Sound like your brother was facing a lot more time and took the best deal he could. Unfortunately, I can't count how many times I have seen family members crying in the courtroom as their family members is sentenced to double digits in state prison. All I can think is -- where were they when their family member was growing up? Didn't anyone teach them right from wrong? It's a little late to be crying now that the crime has been committed and it's all over.
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All three of my colleagues make valid and important points. The bottom line is your brother took a plea, the consequences of which I presume were fully explained to him by his attorney and then the court. If so, that ends the case, absent a constitutional violation.
As for the video, it's of no relevance if all it does is "explain" why he did the crime. It can only be used in evidence if authenticated and if it shows something that constitutes a legal defense to the charge. "Explaining" why he committed a crime might be used to mitigate the penalty but it has nothing to do with guilt or innocence.
Essentially, if your brother had a defense to the charge available to him, surely he would have fought the case instead of admitting he committed the crime charged? Any idea why he chose not to?
The length of the sentence suggests gang involvement and use of a firearm by a participant. However, without knowing more, it's impossible to give you more than impressions suggested by your brief summary.