Hello student ,

Since both forces have equal magnitude F1 = F2 = F

Since its given that the resultant force is equal to magnitude of one of the two forces F(resultant)= F

Therefore

F(R) = sqrt of F1^2 + F2^2 + 2F1F2Cos(theeta)

Substituting values of F

F = sqrt of F^2 + F^2 + 2F^2Cos(theeta)

Squaring on both sides we get

F^2 = 2F^2[1+Cos(theeta)]

Canceling F^2 on both sides we get

1/2 -1 = Cos(theeta)

Therefore ,

Theeta = cos inverse of  -1/2

= 2Pi/3