If sin 6 theta + sin 4 theta + sin 2 theta = | vedclass

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(A) Given the equation: $\sin 6 	heta + \sin 4 	heta + \sin 2 	heta = 0$Group the terms: $(\sin 6 	heta + \sin 2 	heta) + \sin 4 	heta = 0$Using

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$\frac{n \pi}{4}, n \pi \pm \frac{\pi}{3}$

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(A) Given the equation: $\sin 6 	heta + \sin 4 	heta + \sin 2 	heta = 0$Group the terms: $(\sin 6 	heta + \sin 2 	heta) + \sin 4 	heta = 0$Using the sum-to-product formula $\sin A + \sin B = 2 \sin \frac{A+B}{2} \cos \frac{A-B}{2}$:$2 \sin 4 	heta \cos 2 	heta + \sin 4 	heta = 0$Factor out $\sin 4 	heta$:$\sin 4 	heta (2 \cos 2 	heta + 1) = 0$This gives two cases:Case $1$: $\sin 4 	heta = 0 \implies 4 	heta = n \pi \implies 	heta = \frac{n \pi}{4}$Case $2$: $2 \cos 2 	heta + 1 = 0 \implies \cos 2 	heta = -\frac{1}{2}$Since $\cos \frac{2 \pi}{3} = -\frac{1}{2}$, we have $\cos 2 	heta = \cos \frac{2 \pi}{3}$The general solution for $\cos x = \cos \alpha$ is $x = 2 n \pi \pm \alpha$So, $2 	heta = 2 n \pi \pm \frac{2 \pi}{3}$Dividing by $2$, we get $	heta = n \pi \pm \frac{\pi}{3}$Thus, the general values are $	heta = \frac{n \pi}{4}$ and $	heta = n \pi \pm \frac{\pi}{3}$.

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$k$	$\frac{1}{5}$	$2k$	$\frac{3}{10}$	$k$

If $\sin 6 \theta + \sin 4 \theta + \sin 2 \theta = 0$, then the general value of $\theta$ is

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