[例2](1)(2020·全国卷Ⅲ)已知 sin theta +sin (theta +dfrac (pi )(3))=1,-|||-则 sin (theta +dfrac (pi )(6))= ()-|||-

当theta =dfrac (pi )(3)时，theta =dfrac (pi )(3)______，theta =dfrac (pi )(3)______，

当 theta =dfrac (pi )(3) 时，theta =dfrac (pi )(3)________ ，theta =dfrac (pi )(3)__

dfrac ({v)_(1)}(sin theta )

已知(sin )^2theta -(cos )^2theta =dfrac (2sqrt {2)}(3)，求(sin )^2theta -(cos )^2the

当theta =dfrac (pi )(4)时，theta =dfrac (pi )(4)____;当theta =dfrac (pi )(4)时，theta

9.计算下列积分:-|||-(1) (int )_(0)^2pi dfrac (1)(5+3sin theta )dtheta ;-|||-(2) (int

(7) (int )_(0)^pi (1-(sin )^3theta )dtheta ;

[题目]已知 tan theta -tan (theta +dfrac (pi )(4))=7, 则 tan theta =-|||-()-|||-

(8) int_(0)^pi(1-sin ^3theta )dtheta(8) $\int_{0}^{\pi}(1-\sin ^{3}\theta )d\the

(sin x)=dfrac (1)({cos )^2x} in (0,dfrac (pi )(2)),则(sin x)=dfrac (1)({cos )^2x}