Thanks for the update. In the argument for Cosine, i mean two angles, phii and phic. Its not the product of phi and c (because c is the RHS of eq. 3). So, I got the output but as I have very little knowledge of Mathematica, I have problem interpreting the result. I have attached the notebook.
{{Ll -> -((\[Sqrt](-8 a^2 b Cos[c \[Phi]]^4 +
OutputSizeLimit`Skeleton[377] + OutputSizeLimit`Skeleton[
1] - \[Sqrt]((8 a^2 b Cos[c \[Phi]]^4 -
16 a b^2 Cos[c \[Phi]]^4 + OutputSizeLimit`Skeleton[
373])^2 -
4 (OutputSizeLimit`Skeleton[195] +
16 a^2 c^2 OutputSizeLimit`Skeleton[
1]^4 Cos[OutputSizeLimit`Skeleton[1]]^4) (16 b^2 Cos[
c \[Phi]]^4 - 32 b c Cos[c \[Phi]]^4 +
16 c^2 Cos[c \[Phi]]^4 + OutputSizeLimit`Skeleton[
282] + 16 a^2 Cos[c \[Phi] - i \[Phi]]^8 -
32 a b Cos[c \[Phi] - i \[Phi]]^8 +
16 b^2 Cos[c \[Phi] - i \[Phi]]^8))))/(Sqrt[
2] \[Sqrt](16 b^2 Cos[c \[Phi]]^4 - 32 b c Cos[c \[Phi]]^4 +
16 c^2 Cos[c \[Phi]]^4 + 32 b c Cos[c \[Phi]]^6 -
32 c^2 Cos[c \[Phi]]^6 + OutputSizeLimit`Skeleton[276] +
32 a c Cos[c \[Phi]] Cos[i \[Phi]] Cos[
c \[Phi] - i \[Phi]]^7 -
32 b c Cos[c \[Phi]] Cos[i \[Phi]] Cos[
c \[Phi] - i \[Phi]]^7 +
16 a^2 Cos[c \[Phi] - i \[Phi]]^8 -
32 a b Cos[c \[Phi] - i \[Phi]]^8 +
16 b^2 Cos[c \[Phi] - i \[Phi]]^8))),
Mm -> OutputSizeLimit`Skeleton[1]/(
OutputSizeLimit`Skeleton[1] + OutputSizeLimit`Skeleton[233] +
OutputSizeLimit`Skeleton[1]),
Xx -> OutputSizeLimit`Skeleton[1]/OutputSizeLimit`Skeleton[
1]}, {OutputSizeLimit`Skeleton[1]}, OutputSizeLimit`Skeleton[
1], {OutputSizeLimit`Skeleton[1]}}
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