#(2-(cosx)/(1.341))^2((-sinx)/1.341)^2 = 1#
#(2\times 1.341 - cosx)^2(sin^2x) = 1\times(1.341)^4#
#(7.1931 - 5.364 cos x + cos^2x)(sin^2x) = 3.2338#
Let us use #sin^2x + cos^2x = 1# as #sin^2x = 1-cos^2x#. Then
#(7.1931 - 5.364 cos x + cos^2x)(1-cos^2x) = 3.2338#
#(-cos^4x + 5.364 cos^3x -7.1931cos^2x + cos^2x -5.364 cosx +7.1931 - 3.2338) = 0#
#(cos^4x - 5.364 cos^3x +6.1931cos^2x+5.364 cosx -3.9593) = 0#
Let #y = cosx# then we have a fourth order polynomial. Solving this leads to 4 solutions for #cos x# You can find the #x# as #cos^(-1) y#. I have the solutions as
#y = 2.8418 \pm 0.6332 i, -0.8617, 0.5421#
