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P(0) = P(π) = (0,4)
P(α) = P(β) = (√2,6-2√2)

sinα = {1+√(√2 -1)} /2 = 0.821797126452791
sinβ = {1-√(√2 -1)} /2 = 0.178202873547209

cosα = {(1-√2) +√(1+√2)} /2 = 0.5697802058284711
cosβ = {(1-√2) -√(1+√2)} /2 = -0.983993768201566

cos(2α) = sin(2β) = 1 -1/√2 -√(√2 -1) = -0.35070103409213
sin(2α) = cos(2β) = 1 -1/√2 +√(√2 -1) = 0.936487474717190

α + β = (5/4)π