What is 3(sin x − cos x)⁴ + 6(sin x + cos x)² + 4(sin x)⁶ + 4(cos x)⁶ equal to?

Let s = sin²x, c = cos²x with s+c = 1. (sinx−cosx)⁴ = (1−2sinxcosx)² = 1−4sc·... Use: 4(sin⁶+cos⁶) = 4(1−3sc) = 4−12sc where sc=sinxcosx... actually sin⁶+cos⁶ = 1−3sin²xcos²x. So 4(sin⁶x+cos⁶x) = 4−12sin²xcos²x. (sinx−cosx)⁴ = (1−2sinxcosx)² = 1−4sinxcosx+4sin²xcos²x. ×3 = 3−12sinxcosx+12sin²xcos²x. (sinx+cosx)² = 1+2sinxcosx. ×6 = 6+12sinxcosx. Sum: 3−12sxcx+12s²c²+6+12sxcx+4−12s²c² = 13.