sin^4A+cos^4A
=(sin²A+cos²A)²-2sin²Acos²A)
=1²-2(sinAcosA)²
=1-2(1/2*sin2A)²=5/9
(1/2*sin2A)²=2/9
sin²A=8/9
sinA=-2√2/3,sinA=2√2/3