If the solution of the equation log_cos x cot x+4 log_sin x tan x=1, x ∈(0, (π)/2), is sin^-1((α+√ β)/2), where α, β are integers, then α+β is equal…

If the solution of the equation $\displaystyle \log _{\cos x} \cot x+4 \log _{\sin x} \tan x=1, x \in\left(0, \frac{\pi}{2}\right)$, is $\displaystyle \sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)$, where $\displaystyle \alpha$, $\displaystyle \beta$ are integers, then $\displaystyle \alpha+\beta$ is equal to :