Step 1: Read the twist in the question.
Nitroglycerine is supposed to ease chest pain by relaxing the veins and easing the heart's load. Here it does the opposite and makes the pain worse, so this cannot be a plain case of coronary artery blockage.
Step 2: Recall what makes a heart condition react this way.
In hypertrophic obstructive cardiomyopathy the thickened muscle wall already blocks the path blood takes out of the heart. Nitroglycerine reduces the blood returning to the heart and the resistance it pumps against, which shrinks the ventricle even further and tightens that blockage, worsening the pain instead of relieving it.
Step 3: Weigh the family history.
A brother who died suddenly at 40 fits the inherited pattern of hypertrophic cardiomyopathy, which runs in families and is a leading cause of sudden cardiac death in relatively young people.
Step 4: Cross off the other diagnoses.
Endocarditis comes with fever and a changing murmur, not this specific nitrate reaction. Mitral regurgitation from wear and tear causes breathlessness and a regurgitant murmur, without this family pattern of sudden death. Aortic dissection causes sudden tearing pain radiating to the back, and does not show this particular worsening with nitroglycerine.
Step 5: Conclude.
$\boxed{\text{Hypertrophic obstructive cardiomyopathy}}$