The hadronic $$\tau $$ τ decay $$\tau ^-\rightarrow K_1^-\nu _\tau \rightarrow (K^-\omega ) \nu _\tau \rightarrow (K^- \pi ^+\pi ^-\pi ^0)\nu _\tau $$ τ - → K 1 - ν τ → ( K - ω ) ν τ → ( K - π + π - π 0 ) ν τ and the axial vector mixing angle

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