If e[sin2⁡α+sin4⁡α+sin6⁡α+...∞] loge⁡2 is a root of equation x2-9x+8=0, where 0<α<π2, then the principle value of sin-1⁡sin⁡2π3 is

Question

e^{[\sin^{2} α + \sin^{4} α + \sin^{6} α + . . . \infty] \log_{e} 2}

is a root of equation

x^{2} - 9 x + 8 = 0,

where

0 < α < \frac{π}{2},

then the principle value of

\sin^{- 1} (\sin (\frac{2 π}{3}))

α

2 α

- α

- 2 α

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