9.
\((1)\)函数\(y=\ln (2\sin x-\sqrt{2})\)的定义域是______ .
\((2)\)已知函数\(f(x){=}x^{2}{-}2x\sin\theta{+}1\)有零点,则\(\theta\)角的取值集合为______ .
\((3)\)若直线\(l_{1}\):\(6x{+}my{-}1{=}0\)与直线\(l_{2}\):\(2x{-}y{+}1{=}0\)平行,则\(m{=}\)______ .
\((4)\)求函数\(f(x){=}2\sin(x{+}\dfrac{\pi}{4})\),给出下列四个命题:
\({①}\)存在\(\alpha{∈}({-}\dfrac{\pi}{2}{,}0)\)使\(f(\alpha){=}\sqrt{2}\);
\({②}\)存在\(\alpha{∈}(0{,}\dfrac{\pi}{2})\),使\(f(x{-}\alpha){=}f(x{+}\alpha)\)恒成立;
\({③}\)存在\(\alpha{∈}R\),使函数\(f(x{+}\alpha)\)的图象关于坐标原点成中心对称;
\({④}\)函数\(f(x)\)的图象关于直线\(x{=-}\dfrac{3\pi}{4}\)对称;
\({⑤}\)函数\(f(x)\)的图象向左平移\(\dfrac{\pi}{4}\)个单位就能得到\(y{=-}2\cos x\)的图象\(.\)其中正确的序号是______ .