α_1, β_1 be the roots of x^2-2x sec⁡θ+1=0, α_2, β_2 be of x^2+2x tan⁡θ-1=0. Find α_1+β_2.

Let, α_1, β_1 be the roots of the equation x^2-2x sec⁡θ+1=0 and α_2, β_2 be the roots of the equation x^2+2x tan⁡θ-1=0, where -π/6 less than θ less than -π/12 . If α_1 greater than β_1 and α_2 greater than β_2, find α_1+β_2.
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