Re-installing Windows(Broken Laptop Screen)

So my computer has been running awful as of late, games have started to run slowly and i can't even defrag my computer anymore.
So i've decided to just format the entire thing, and reinstall windows.

But the problem is that my laptop screen is broken, it is connected to a Samsung 22'' monitor via HDMI, but it doesn't start to show anything before it enters windows, and apparently there's no way to fix this.

So my question is, is there anyway to format my drive and re-install windows while being in windows?

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Forgot to add

It's Windows 7.

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Sadly no.

While a few have used the Fn key to enable an external VGA this issue while widely discussed usually ends with "fix the machine" to install Windows.

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