I'm not sure if you are still interested, but I believe the equation you are looking for is:
$$F = \frac{2sin(θ)EI}{L^2}$$$$F = \frac{2\sin(θ)EI}{L^2}$$
where θ is the angle at the end of your cantilever. I base this equation #16 from the paper, "An integral approach for large deflection cantilever beams"