3.
\((1)\)如图,已知\(\vartriangle ABC\)中,\(D\)为边\(BC\)上靠近\(B\)点的三等分点,连接\(AD\),\(E\)为线段\(AD\)的中点,若\(\overrightarrow{CE}=m\overrightarrow{AB}+n\overrightarrow{AC}\),则\(m+n=\) .
\((2)\)方程\(\left| \dfrac{2x+3}{x+1} \right|={{(x+2)}^{2}}\) 解的个数为 .
\((3)\)已知\(\tan (\theta +\dfrac{\pi }{2})=2,\) 则\(\sin \theta \cos \theta =\) .
\((4)\)已知\(\omega > 0,A > 0,a > 0,0 < \varphi < \pi ,y=\sin x\) 的图象按照以下次序变换:\(①\)纵坐标不变,横坐标变为原来的\(\dfrac{1}{\omega }\) ;\(②\)向左移动\(\varphi \) 个单位;\(③\)向上移动\(a\) 个单位;\(④\)纵坐标变为\(A\) 倍\(.\)得到\(y=3\sin (2x-\dfrac{\pi }{6})+1\) 的图象,则\(A+a+\omega +\varphi =\) .