If sin⁡θ1sin⁡θ2−cos⁡θ1cos⁡θ2+1=0then the value of tan⁡θ1/2cot⁡θ2/2is equal to ______

Solution:

$\begin{array}{l} \sin θ_{1} \sin θ_{2} - \cos θ_{1} \cos θ_{2} = - 1 or \\ \cos (θ_{1} + θ_{2}) = 1 \Rightarrow θ_{1} + θ_{2} = 2 nπ, n \in I or \frac{θ_{1}}{2} + \frac{θ_{2}}{2} = nπ \\ Thus, \tan \frac{θ_{1}}{2} \cot \frac{θ_{2}}{2} = \tan \frac{θ_{1}}{2} \cot (nπ - \frac{θ_{1}}{2}) \\ = - \tan \frac{θ_{1}}{2} \cot \frac{θ_{1}}{2} = - 1 \end{array}$

If $\sin θ_{1} \sin θ_{2} - \cos θ_{1} \cos θ_{2} + 1 = 0$ then the value of $\tan (θ_{1} / 2) \cot (θ_{2} / 2)$ is equal to ______

Solution:

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