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I am using stress-energy tensor to derive equation of state of photon gas (assuming it as a perfect fluid).

I completed all the steps except one:

average value of [cos(θ)]^2 over unit sphere = 1/3.

I have no idea how this is so. (θ is polar angle).

I tried integrating over 0<θ<∏ and 0<φ<2∏, and then divided by the surface area of the sphere, but no luck with that either...

Please help!

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# Equation of state of photon gas

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