Question: Cannot solve the equation

I cannot solve the equation. The problem is:

we have the integrals (1) and variable (2)
(1) F := (a1, b1) -> int(1/sqrt(1 + (-1)*b1^2*sin(teta)*sin(teta)), teta = 0 .. a1)

(2) Phi(Pi/2, teta) = 2*(F((Pi/2 - teta_l)/2, sqrt(2/(1 - sin(teta_l)))) - F1(Pi/4, sqrt(2/(1 - sin(teta_L)))))/sqrt(sin(teta_l) - 1)

After the solution for variable (2) I received: 

(-InverseJacobiAM(-Pi/4 + teta_l/2, 1/abs(cos(Pi/4 + teta_l/2))) - InverseJacobiAM(Pi/4, 1/abs(cos(Pi/4 + teta_l/2))))^2/(2*(sin(teta_l) - 1))

Next, I have the equation and (by the followed paper) should solve the equation respect to teta_l

M*B*(L/C)^2/G = 1/8*Phi(Pi/2, teta_l)^2

But I received just empty solution. The reference paper 10.1016/j.jmps.2020.104045

Can somebody recommend the way to solve the problem?