Let →a,→b and →c are three unit vectors such that →a+→b+→c is also a unit vector. If pairwise angle between →a,→b and →c are θ1,θ2 and θ3 respectively such that sin2(θ12)+sin2(θ22)+sin2(θ32)=α, then the value of α2 is

Let →a,→b and →c are three unit vectors such that →a+→b+→c

1.	Let →a,→b and →c are three unit vectors such that →a+→b+→c is also a unit vector. If pairwise angle between →a,→b and →c are θ1,θ2 and θ3 respectively such that sin2(θ12)+sin2(θ22)+sin2(θ32)=α, then the value of α2 is
Answer» Let $\to a, \to b$ and $\to c$ are three unit vectors such that $\to a + \to b + \to c$ is also a unit vector. If pairwise angle between $\to a, \to b$ and $\to c$ are $θ_{1}, θ_{2}$ and $θ_{3}$ respectively such that ${sin}^{2} (\frac{θ_{1}}{2}) + {sin}^{2} (\frac{θ_{2}}{2}) + {sin}^{2} (\frac{θ_{3}}{2}) = α,$ then the value of $α^{2}$ is