[GK2018,national I,19]Analytic geometry and ellipse

Let $F$ be the right focus of the ellipse: $\frac{x^{2}}{2}+y^{2}=1$ .

A line passing $F$ intersects with the ellipse at point $A,B$ , another point $M$ is at $(2,0)$ ,as shown in the picture.

Is it always true that $\angle OMA=\angle OMB?$

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This problem is from GK2018 ,also known as GaoKao, or College entrance examination in China.

It's from national I volume and it's the 19th problem.