$\sin{3\theta} \,=\, 3\sin{\theta}-4\sin^3{\theta}$
$3\sin{\theta}-4\sin^3{\theta} \,=\, \sin{3\theta}$
It is called sine triple angle formula and used in two different cases.
Sine triple angle identity is used to either expand or simplify the triple angle trigonometric functions like $\sin{3x}$, $\sin{3A}$, $\sin{3\alpha}$ and etc. For example,
$(1) \,\,\,\,\,\,$ $\sin{3x} \,=\, 3\sin{x}-4\sin^3{x}$
$(2) \,\,\,\,\,\,$ $\sin{3A} \,=\, 3\sin{A}-4\sin^3{A}$
$(3) \,\,\,\,\,\,$ $\sin{3\alpha} \,=\, 3\sin{\alpha}-4\sin^3{\alpha}$
Learn how to derive the rule of sin triple angle identity by geometrical approach in trigonometry.
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