Properties Of Triangles

Let \(\alpha\) be the solution of \({16^{{{\sin }^2}\theta }} + {16^{{{\cos }^2}\theta }} = 10\) in \(\left( {0,{\pi \over 4}} \right)\). If the shadow of a vertical pole is \({1 \over {\sqrt 3 }}\) of its height, then the altitude of the sun is