what is the gravitational deflection of light with this first order approximation of Schwarzschild metric

Question

The gravitational deflection of light results from the effects of general relativity is an important calculation.

Now, I'm wondering, if I were using a first-order approximation of the Schwarzschild metric at the very beginning, namely 

$$ds^2 = -\frac{1}{(1+\frac{r_s}{r})}c^2dt^2 + (1+\frac{r_s}{r})dr^2 + r^2d\theta^2 + r^2sin^2\theta d\phi^2.$$

Would that lead to the same gravitational deflection of light or would that lead to a different result? 

Comments

Your metric doesn't look like Schwarzschild, nor like a linearisation thereof. As for your question: Do the calculation!