Consider the system of equations : `x sintheta-2ycostheta-az=0`, `x+2y+z=0`, `-x+y+z=0`, `theta in R`

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

The number of integral values of a for which the system of linear equations x sin theta -2 y cos theta -az=0 , x+2y+z=0,-x+y+z=0 may have non-trivial solutions, then

Consider the system of equations in x, y, z as x sin3theta-y+z =0 x cos 2 theta+4 y+3 z =0 2 x+7 y+7 z =0 If this system has a non-trivial solution, then for any integer n, values of theta are given

Consider the system of equations in x, y, z as x sin 3 theta-y + z=0, x cos 2 theta+ 4y + 3z= 0 , 2x + 7y + 7z = 0. If this system has a non-trival solution, then for integer n, values of theta are given by :

Number of values of theta lying I [0,100 pi ] for which the system of equations (sin 3 theta ) x-y+z=0, (cos 2 theta ) x+4y +3z=0, 2x+ 7y+7z =0 has non-trivial solution is "____"

Number of values of theta lying I [0,100 pi ] for which the system of equations (sin 3 theta ) x-y+z=0, (cos 2 theta ) x+4y +3z=0, 2x+ 7y+7z =0 has non-trivial solution is "____"