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**How did you find PF?:**internet question about electron triplet states

I'm a retired accelerator physicist entertaining myself by trying to understand physics questions like entanglement better. I calculate the expectation value of the product of two electron spins in the singlet state with measurement #1 at arbitrary angle

__phi__wrt z-axis, #2 measurement angle

__phi+ theta__, getting the -cos(theta) answer independent of phi that I expected, as per Bell's theorem experiments. But with Susskind's ("Quantum Mechanics Theoretical Minimum")

__maximally entangled triplet__states, I get either cos(theta) or cos (theta+2*phi). I'm doubtful that my results are correct. What are the answers and where are they worked out?