Solve for $x$ on the indicated domain.

1. $2 \sin(x) + \sqrt { 2 }= 0,$$\: 0 ≤ x < 2π$

   Step (a):

   $\sin(x)=-\frac{\sqrt{2}}{2}$

2. $\cos(x)(2 \sin(x) +\sqrt { 2 })= 0,$$\: 0 ≤ x < 2π$

   Step (b):

   $\cos(x)=0\text{ or }2\sin(x)+\sqrt{2}=0$

3. $\cos(x)(2 \sin(x) +\sqrt { 2 }) = 0$

   Hint (c):

   Adjust your answer from part (b) to include all solutions.