Suppose $\omega$ is a Kähler metric of constant scalar curvature with positive bisectional curvature, how to prove $\omega$ is Kähler-Einstein?

I was told that we can use the following method:

Step 1: Use Bochner tecnique to prove $\dim H^2=1$

Step 2: Constant scalar curvature $\implies$ Ricci curvature is coclosed.

Step 3: Using Hodge theorem to derive the result.

Related reference:

On the Second Cohomology Group of a Kaehler Manifold of Positive Curvature

How can we prove this in detail? Or where can I find further reference for this?

**Update:**

I heard this is a famous result from Hongxi Wu and his partner, and it can be proved using Weitzenbock method.