Calling all mathematicians! Can you answer this question?

You are not allowed a calculator and have between 6-8 minutes to answer it

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NudasPriest · 46-50, M

Rough scratching my working gave:

(arccos(0.5))/pi - 2*squareroot(12)

High likelihood of mistakes.

Yes, errors. More like:

8*sqrt(12) - 16pi/3