解：因为 (sin θ)^2 +(cos θ)^2 =1,
且 (sin θ)^4 +(cos θ)^4 =5/9,
所以 1 = [ (sin θ)^2 +(cos θ)^2 ]^2
= (sin θ)^4 +(cos θ)^4 +2 (sin θ)^2 (cos θ)^2
= 5/9 +(1/2) *(2 sin θ cos θ)^2
= 5/9 +(1/2) *(sin 2θ)^2.
解得 sin 2θ = ±2√2 /3.
= = = = = = = = =
注意：
2 (sin θ)^2 (cos θ)^2
= (1/2) *(2 sin θ cos θ)^2
= (1/2) *(sin 2θ)^2.
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