如何用双正弦曲线拟合数据——第二部分

针对单正弦函数 $a\sin(b+xc)$ 的拟合，我看到一篇论文里用两次积分法求解参数c的方案简洁有效。但尝试用同样方法处理双正弦函数 $a_1\sin(b_1+xc_1)+a_2\sin(b_2+xc_2)$ 时，求解 $c_1$ 和 $c_2$ 的表达式变得异常复杂，怀疑是不是自己思路绕远了。想请教：这种情况还能用论文里的积分法解决，还是必须采用迭代法？

实验数据 #

x = [0.        , 0.02564103, 0.05128205, 0.07692308, 0.1025641 ,
   0.12820513, 0.15384615, 0.17948718, 0.20512821, 0.23076923,
   0.25641026, 0.28205128, 0.30769231, 0.33333333, 0.35897436,
   0.38461538, 0.41025641, 0.43589744, 0.46153846, 0.48717949,
   0.51282051, 0.53846154, 0.56410256, 0.58974359, 0.61538462,
   0.64102564, 0.66666667, 0.69230769, 0.71794872, 0.74358974,
   0.76923077, 0.79487179, 0.82051282, 0.84615385, 0.87179487,
   0.8974359 , 0.92307692, 0.94871795, 0.97435897, 1.        ]
y = [2.98994949, 2.45766647, 1.51829117, 0.57449757, 0.15340313,
       0.64032065, 2.04580719, 3.93814129, 5.59607034, 6.3244815 ,
       5.7865173 , 4.18760477, 2.21232589, 0.73341424, 0.4246889 ,
       1.45943814, 3.43671601, 5.5689522 , 7.03928712, 7.35809663,
       6.55364103, 5.11721008, 3.74409743, 3.00704441, 3.12199756,
       3.90873324, 4.94401238, 5.80843722, 6.28943297, 6.43890658,
       6.47205068, 6.58358129, 6.80015951, 6.96078318, 6.83721446,
       6.31988894, 5.55089141, 4.91051686, 4.84543347, 5.62019942]

内容的提问来源于Stack Exchange，提问作者nopeva