(sin(2*x))*(sin(2*x))+(sin(4*x))*(sin(4*x))+(sin(6*x))*(sin(6*x))=2

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Solution for (sin(2*x))*(sin(2*x))+(sin(4*x))*(sin(4*x))+(sin(6*x))*(sin(6*x))=2 equation: 


Simplifying
(sin(2x))(sin(2x)) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (2x)
(ins * 2x)(sin(2x)) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
(2ins * x)(sin(2x)) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Multiply ins * x
(2insx)(sin(2x)) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (2insx)
2insx(sin(2x)) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (2x)
2insx(ins * 2x) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
2insx(2ins * x) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Multiply ins * x
2insx(2insx) + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (2insx)
2insx * 2insx + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
2 * 2insx * insx + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Multiply 2 * 2
4insx * insx + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Multiply insx * insx
4i2n2s2x2 + (sin(4x))(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (4x)
4i2n2s2x2 + (ins * 4x)(sin(4x)) + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + (4ins * x)(sin(4x)) + (sin(6x))(sin(6x)) = 2

Multiply ins * x
4i2n2s2x2 + (4insx)(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (4insx)
4i2n2s2x2 + 4insx(sin(4x)) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (4x)
4i2n2s2x2 + 4insx(ins * 4x) + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + 4insx(4ins * x) + (sin(6x))(sin(6x)) = 2

Multiply ins * x
4i2n2s2x2 + 4insx(4insx) + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (4insx)
4i2n2s2x2 + 4insx * 4insx + (sin(6x))(sin(6x)) = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + 4 * 4insx * insx + (sin(6x))(sin(6x)) = 2

Multiply 4 * 4
4i2n2s2x2 + 16insx * insx + (sin(6x))(sin(6x)) = 2

Multiply insx * insx
4i2n2s2x2 + 16i2n2s2x2 + (sin(6x))(sin(6x)) = 2

Remove parenthesis around (6x)
4i2n2s2x2 + 16i2n2s2x2 + (ins * 6x)(sin(6x)) = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + 16i2n2s2x2 + (6ins * x)(sin(6x)) = 2

Multiply ins * x
4i2n2s2x2 + 16i2n2s2x2 + (6insx)(sin(6x)) = 2

Remove parenthesis around (6insx)
4i2n2s2x2 + 16i2n2s2x2 + 6insx(sin(6x)) = 2

Remove parenthesis around (6x)
4i2n2s2x2 + 16i2n2s2x2 + 6insx(ins * 6x) = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + 16i2n2s2x2 + 6insx(6ins * x) = 2

Multiply ins * x
4i2n2s2x2 + 16i2n2s2x2 + 6insx(6insx) = 2

Remove parenthesis around (6insx)
4i2n2s2x2 + 16i2n2s2x2 + 6insx * 6insx = 2

Reorder the terms for easier multiplication:
4i2n2s2x2 + 16i2n2s2x2 + 6 * 6insx * insx = 2

Multiply 6 * 6
4i2n2s2x2 + 16i2n2s2x2 + 36insx * insx = 2

Multiply insx * insx
4i2n2s2x2 + 16i2n2s2x2 + 36i2n2s2x2 = 2

Combine like terms: 4i2n2s2x2 + 16i2n2s2x2 = 20i2n2s2x2
20i2n2s2x2 + 36i2n2s2x2 = 2

Combine like terms: 20i2n2s2x2 + 36i2n2s2x2 = 56i2n2s2x2
56i2n2s2x2 = 2

Solving
56i2n2s2x2 = 2

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Divide each side by '56n2s2x2'.
i2 = 0.03571428571n-2s-2x-2

Simplifying
i2 = 0.03571428571n-2s-2x-2

Take the square root of each side:
i = {-0.188982236n-1s-1x-1, 0.188982236n-1s-1x-1}

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