∵sina+cosa=1/3
∴sin²a+cos²a+2sinacosa=1/9
1+2sinacosa=1/9
sinacosa=-4/9
∴tan³a+cot³a
=sin³a/cos³a+cos³a/sin³a
=(sin^6a+cos^6a)/sin³a*cos³a
分子=(sin²a+cos²a)³-3sin^4acos²a-3sin²acos^4a
=1-3sin²cos²(sin²a+cos²)
=1-3*(sinacosa)²*1
=11/27
分母=(sinacosa)³=-64/729
所以原式=-297/64