For `0 lt theta lt pi/2`, the solutions of `sigma_(m-1)^(6)"cosec"(theta+((m-1)pi)/4)" cosec "(theta+(mpi)/4)=4sqrt(2)` is (are):

Options

A. `pi/4`
B. `pi/6`
C. `pi/12`
D. `(5pi)/12`

Explanation

To solve the equation

\[ \sum_{m=1}^{6} \csc\left(\theta + \frac{(m-1)\pi}{4}\right) \csc\left(\theta + \frac{m\pi}{4}\right) = 4\sqrt{2} \]

for \(0 < \theta < \frac{\pi}{2}\), we will follow these steps:

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