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

( 10 ) (int )_(0)^dfrac (pi {4)}(tan )^2theta dtheta ;

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

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)______，

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

计算下列积分:-|||-(9) (int )_(-e)^-2dfrac (dx)(1+x);-|||-(10) (int )_(0)^dfrac (pi {4)

tan dfrac (pi )(6)= ()-|||-

1357.已知 tan x=1, in (dfrac (pi )(2),dfrac (3pi )(2)), 则 =-|||-

(8) lim _(xarrow dfrac {pi )(2)}dfrac (tan x)(tan 3x)

(8) lim _(xarrow dfrac {pi )(2)}dfrac (tan x)(tan 3x)