How to find the sum with Mathematica?

That hard problem was invented by V. P. Beshkarev (Russia) in 1971:

Sum[Tan[(4*j - 3)*Pi/180], {j, 1, 45}] // FullSimplify 

The result should be 45, but the command is running on my comp without any output for hours. I know its tricky calculation by hand which cannot be mimicked with Mathematica.