ANSWER
[tex]\frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{4}, \frac{7\pi}{4}[/tex]
EXPLANATION
Given;
[tex]2\sin \left(θ\right)\cos \left(θ\right)+\sqrt{2}\cos \left(θ\right)=0[/tex]
Factorise cos ;
[tex]\cos \left(θ\right)\left(2\sin \left(θ\right)+\sqrt{2}\right)=0[/tex]
Solving separately, we have;
[tex]\begin{gathered} \cos\left(θ\right)=0 \\ or \\ 2\sin \left(θ\right)+\sqrt{2}=0 \\ \end{gathered}[/tex][tex]cos(\theta)=0\text{ }[/tex]
Cos theta will only be zero when angle is;
[tex]\frac{\pi}{2},\frac{3\pi}{2}[/tex]
SOolving for;
[tex]\:2\sin \left(θ\right)+\sqrt{2}=0[/tex]
The solution is;
[tex]\begin{gathered} \begin{equation*} 2\sin\left(θ\right)+\sqrt{2}=0 \end{equation*} \\ =θ=\frac{5\pi}{4},\frac{7\pi}{4} \end{gathered}[/tex]
Hence, combining the two solutions , we have;
[tex]\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{4},\frac{7\pi}{4}[/tex]
ANSWER
