If the tangent at a point $$\left( {4\cos \phi ,{{16} \over {\sqrt {11} }}\sin \phi } \right)$$ to the ellipse $$16{x^2} + 11{y^2} = 256$$ is also a tangent to $${x^2} + {y^2} - 2x = 15$$, then $$\phi$$ equsls