已知 α,β∈(0,π2)\alpha ,\beta \in \left( {0,\frac{\pi }{2}}\right)α,β∈(0,2π) ,且 sinα−sinβ=−12\sin \alpha - \sin \beta = - \frac{1}{2}sinα−sinβ=−21 , cosα−cosβ=12\cos \alpha - \cos \beta = \frac{1}{2}cosα−cosβ=21 ，则 tanα+tanβ=\tan \alpha + \tan \beta =tanα+tanβ= ___.