On page 457 it was shown that for a spin echo applied to an I3S spin system the amount of the singly anti-phase terms goes as cos2 (2πJ τ) sin (2πJ τ). Maximizing this function is equivalent to finding the maximum in cos2 (θ) sin (θ) where θ - 2πJ τ. By differentiating the function cos2 (θ) sin (θ) with respect to θ show that one of the extrema is at sin θ = √1/3, and hence show that the greatest amount of the singly anti-phase term is found when
τ = 0.0980/J. [The calculation is made easier if you use the identity sin2(θ) + cos2 (θ) = 1 so that the expressions can be written entirely in terms of cos(θ) or sin(θ), as is convenient.]
Similarly show that the maximum amount of the doubly anti-phase term, which goes as cos (2πnJ τ) sin2 (2πJ τ), occurs when τ = 0.152/J.