I derived the following trigonometrical equation from a real triangle, knowing that the angle $\alpha$ is an acute one:
$\sin 3\alpha = 2\sin\alpha$
Just by eye-balling the equation, and remembering the trigonometric unit circle, I know that:
$\sin 90 = 1 = 2\sin 30 = 2 \cdot 0.5 = 1$
Therefore, $\alpha = 30^\circ$ is a possible solution.
I am unaware of any trigonometric identity to help me simplify this equation in order to get all possible solutions for $\alpha$, and this intuitive solution is the best I can come up with. I plugged this equation into symbolab.com, but their solution seems very long-winded, and I am hoping for the possibility that a simpler one exists.
How can I solve this type of problem when the intuitive approach fails?