Question: transcendental equation

Hello everyone I am trying to solve the transcendental equation by using the regular false position method cannot succeed. is their nay can solve it form me...

F := ((-288*(lambda + (2*k)/3 - 2/3)*sqrt(2)*lambda^2*arctan(sqrt(4*lambda/(1 - k) - 2)*sqrt(2)/2)/(1 - k)^2 - 144*(lambda + (2*k)/3 - 2/3)*Pi*lambda^2*sqrt(2)/(1 - k)^2 - 36*((lambda + (2*k)/3 - 2/3)*(4*lambda/(1 - k) - 2) + (10*lambda)/3 + (4*k)/3 - 4/3)*sqrt(4*lambda/(1 - k) - 2))*(1 - k)^2)/(256*lambda^2)

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