If $\frac{a x+5}{\left(x^2+b\right)(x+3)}=\frac{x+21}{12\left(x^2+b\right)}+\frac{c}{12(x+3)}$, then $b^2=$

If $2 \sin x-\cos 2 x=1$, then $\left(3-2 \sin ^2 x\right)=$

If $\left(\frac{\sin 3 \theta}{\sin \theta}\right)^2-\left(\frac{\cos 3 \theta}{\cos \theta}\right)^2=a \cos b \theta$, then $a: b=$