Assuming this setup:
15% TA (Apoc atma)
25% DA (10 /war, 5 brutal, 3 atheling, 2 pole grip, 5 VV atma)
45% Zanshin (base SAM main rate if wiki isn't lying, no merits)
If Zanshin can only proc exclusively against DA/TA, and checks last:
Multihit rate = (15%) + ((1-15%) * 25%) + ((1-((1-15%)+(1-15%)*25%))*45%) = .15 (TA) + .2125 (DA) + .287 (Zanshin) = ~65%
Attacks per round = 1 + (.15 * 2) + (.2125 * 1) + (.287 * 1) = 1 + .3 + .2125 + .287 = 1.7995
If Zanshin can only proc exclusively against DA/TA, and check first:
Multihit rate = (45%) + ((1-45%) * 15%) + ((1-((1-45%) + (1-45%) * 15%)) * 25%) = .45 (Zanshin) + .0825 (TA) + .117 (DA) = ~65%
Attacks per round = 1 + (.45 * 1) + (.0825 * 2) + (.117 * 1) = 1.732
If Zanshin can proc mutually with DA/TA, but only on the first hit:
Multihit rate = (15%) + ((1-15%) * 25%) + ((1-((1-15%)+(1-15%)*25%))*45%) = .15 (TA) + .2125 (DA) + .287 (Zanshin) = ~65%
Attacks per round = 1 + (.15 * 2) + (.2125 * 1) + .45 = 1.9625
If Zanshin can proc mutually with DA/TA, on any of the hits:
Multihit rate = (15%) + ((1-15%) * 25%) + ((1-((1-15%)+(1-15%)*25%))*45%) = .15 (TA) + .2125 (DA) + .287 (Zanshin) = ~65%
Attacks per round = (1 + (.15 * 2) + (.2125 * 1)) * 1.45 = 2.19
Honestly, case 1 or 3 seems the most likely. No matter what, you aren't hitting anything like 90% multihit rate total, let alone DA rate, but you are close to averaging 1.9 swings/round.
Edit: Corrected with the info below. Thanks for pointing it out.